Development of Accurate DFT Methods for Computing Redox Potentials of Transition Metal Complexes: Results for Model Complexes and Application to Cytochrome P450

The energetics and evolution of oxidoreductases in deep time

The core metabolic reactions of life drive electrons through a class of redox protein enzymes, the oxidoreductases. The energetics of electron flow is determined by the redox potentials of organic and inorganic cofactors as tuned by the protein environment. Understanding how protein structure affects oxidation-reduction energetics is crucial for studying metabolism, creating bioelectronic systems, and tracing the history of biological energy utilization on Earth. We constructed ProtReDox (https://protein-redox-potential.web.app), a manually curated database of experimentally determined redox potentials. With over 500 measurements, we can begin to identify how proteins modulate oxidation-reduction energetics across the tree of life. By mapping redox potentials onto networks of oxidoreductase fold evolution, we can infer the evolution of electron transfer energetics over deep time. ProtReDox is designed to include user-contributed submissions with the intention of making it a valuable resource for researchers in this field.

Precise Fingerprint Determination of Vibrational Infrared Spectra in a Series of Co(II) Clathrochelates through Experimental and Theoretical Analyses

The energetic demands of modern society for clean energy vectors, such as H2, have caused a surge in research associated with homogeneous and immobilized electrocatalysts that may replace Pt. In particular, clathrochelates have shown excellent electrocatalytic properties for the hydrogen evolution reaction (HER). However, the actual mechanism for the HER catalyzed by these d-metal complexes remains an open debate, which may be addressed via Operando spectroelectrochemistry. The prediction of electrochemical properties via density functional theory (DFT) needs access to thermodynamic functions, which are only available after Hessian calculations. Unfortunately, there is a notable lack in the current literature regarding the precise evaluation of vibrational spectra of such complexes, given their structural complexity and the associated tangled IR spectra. In this work, we have performed a detailed theoretical and experimental analysis in a family of Co(II) clathrochelates, in order to establish univocally their IR pattern, and also the calculation methodology that is adequate for such predictions. In summary, we have observed the presence of multiple common bands shared by this clathrochelate family, using the B3LYP functional, the LANL2DZ basis, and effective core potentials (ECP) for heavy atoms. The most important issue addressed in this article was therefore related to the detailed assignment of the fingerprint associated with cobalt(II) clathrochelates, which is a challenging endeavor due to the crowded nature of their spectra.

Density Functional Theory-Based Protocol to Calculate the Redox Potentials of First-row Transition Metal Complexes for Aqueous Redox Targeting Flow Batteries

Transition metal complexes are a promising class of redox mediators for targeting redox flow batteries due to the tunability of their electrochemical potentials. However, reliable time-efficient tools for the prediction of their reduction potentials are needed. In this work, we establish a suitable density functional theory protocol for their prediction using an initial experimental data set of aqueous iron complexes with bidentate ligands. The approach is then cross-validated using different complexes found in the redox-flow literature. We find that the solvation model affects the prediction accuracy more than the functional or basis set. The smallest errors are obtained using the COSMO-RS solvation model (mean average error (MAE)=0.24 V). With implicit solvation models, a general deviation from experimental results is observed. For a set of similar ligands, they can be corrected using simple linear regression (MAE=0.051 V for the initial set of iron complexes).

A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo

Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low-rank structure of the Coulombic integrals have been successful but exhibit high prefactors, making their utility limited to very large systems. Here we present a complementary cubic-scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to ph-AFQMC. We show that the error due to this approximation, which we term localized-orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable and that the method is computationally favorable even for small systems. We present results demonstrating robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized-orbital-based methods, including the singlet-triplet gaps of the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp)₂. Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp)₂, agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T₀) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T₀) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T₀). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Deciphering Cryptic Behavior in Bimetallic Transition-Metal Complexes with Machine Learning

We demonstrate an alternative, data-driven approach to uncovering structure-property relationships for the rational design of heterobimetallic transition-metal complexes that exhibit metal-metal bonding. We tailor graph-based representations of the metal-local environment for these complexes for use in multiple linear regression and kernel ridge regression (KRR) models. We curate a set of 28 experimentally characterized complexes to develop a multiple linear regression model for oxidation potentials. We achieve good accuracy (mean absolute error of 0.25 V) and preserve transferability to unseen experimental data with a new ligand structure. We also train a KRR model on a subset of 330 structurally characterized heterobimetallics to predict the degree of metal-metal bonding. This KRR model predicts relative metal-metal bond lengths in the test set to within 5%, and analysis of key features reveals the fundamental atomic contributions (e.g., the valence electron configuration) that most strongly influence the behavior of these complexes. Our work provides guidance for rational bimetallic design, suggesting that properties, including the formal shortness ratio, should be transferable from one period to another.

A Density Functional Theory Study on Comparing the Reactivity of [Mn(13-TMC)(OOH)]2+ and [Mn(13-TMC)(O2)]+ for the Sulfoxidation of Thioanisole: Elucidation of Substrate and Non-Redox Metal Ion Effects

The reactivities of [Mn(13-TMC)(OOH)]²⁺ (1) and [Mn(13-TMC)(O₂)]⁺ (2) in the sulfoxidation of thioanisole have been compared using density functional theory methods. The orientation of the 13-TMC ligand and substrate and non-redox metal ion effects have been considered to improve the oxidation efficiency of 1 and 2. In 1, the syn- and anti-orientation of the 13-TMC ligand do not change the coordination of the Mn ion. In contrast, the orientation of the 13-TMC ligand regulates the geometry of 2, wherein the syn-13-TMC ligand exhibits the Mn^III-peroxo (2_hs and 2_ls) species, while the anti-13-TMC shows the Mn^II-superoxo (2'_hs and 2'_ls) species. However, the Mn^II-superoxo species are found to be less stable than the Mn^III-peroxo complexes by around +26.6 kcal/mol. The ground state geometries of 1 and 2 with the syn-13-TMC ligand are found to be more stable in the high- (S = 2) spin states (1_hs and 2_hs) than the low- (S = 1) spin complexes (1_ls and 2_ls), by +15.6 and +25.5 kcal/mol, respectively. The computed mechanistic pathways clearly indicate that the sulfoxidation of thioanisole by 1_hs is kinetically (by +16.6 to +46.1 kcal/mol) and thermodynamically (+14.4 to +56.1 kcal/mol) more preferred than 1_ls, 2_hs, and 2_ls species. This is mainly due to the feasible heterolytic O1-O2 bond cleavage followed by the proton transfer step. In addition, the molecular electrostatic potential analysis indicates that the higher oxidation efficacy of 1_hs than 2_hs is due to the -OOH moiety. The reactivity of 1_hs is further enhanced by incorporating electron donating substituents in thioanisole, wherein the p-NH₂ thioanisole decreases the ΔG^‡ of 1_hs by 28%. Interestingly, the incorporation of non-redox metal ions (Mⁿ⁺ = Sc³⁺, Y³⁺, Mg²⁺, and Zn²⁺) improves the reactivity of 2_hs, wherein the non-redox metal ions tend to bind with the oxygen atoms of 2_hs and subsequently shift the one-electron reduction potential (E⁰_(red) vs SCE) toward the positive side. The positive shift in the E⁰_(red) is more evident in 2_hs-Y³⁺ that significantly decreases the ΔG^‡ of 2_hs by 58.7%, which is in fact lower than the ΔG^‡ of 1_hs by +2.0 kcal/mol. Hence, in the presence of Y³⁺, the reactivity of 2_hs is comparable with 1_hs in the sulfoxidation of thioanisole.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

Directed Design of a AuI Complex with a Reduced Mesoionic Carbene Radical Ligand: Insights from 1,2,3-Triazolylidene Selenium Adducts and Extensive Electrochemical Investigations

Carbene-based radicals are important for both fundamental and applied chemical research. Herein, extensive electrochemical investigations of nine different 1,2,3-triazolylidene selenium adducts are reported. It is found that the half-wave potentials of the first reduction of the selones correlate with their calculated LUMO levels and the LUMO levels of the corresponding triazolylidene-based mesoionic carbenes (MICs). Furthermore, unexpected quasi-reversibility of the reduction of two triazoline selones, exhibiting comparable reduction potentials, was discovered. Through UV/Vis/NIR and EPR spectroelectrochemical investigations supported by DFT calculations, the radical anion was unambiguously assigned to be triazoline centered. This electrochemical behavior was transferred to a triazolylidene-type MIC-gold phenyl complex resulting in a MIC-radical coordinated AuI species. Apart from UV-Vis-NIR and EPR spectroelectrochemical investigations of the reduction, the reduced gold-coordinated MIC radical complex was also formed in situ in the bulk through chemical reduction. This is the first report of a monodentate triazolylidene-based MIC ligand that can be reduced to its anion radical in a metal complex. The results presented here provide design principles for stabilizing radicals based on MICs.

Ab Initio Evaluation of the Redox Potential of Cytochrome c

Various biochemical activities of metabolism and biosynthesis are fulfilled by redox processes with explicit electron exchange, which furnish redox enzymes with high chemical reactivity. However, theoretical investigation of a redox process, which simultaneously involves a complex electronic change at a redox metal center and conformational reorganization of the surrounding protein environment coupled to the electronic change, requires computationally conflicting approaches, highly accurate quantum chemical calculations, and long-time molecular dynamics (MD) simulations, limiting the physicochemical understanding of biological redox processes. Here, we theoretically examined a redox process of cytochrome c by means of a hybrid molecular simulation technique, which enables one to consistently treat the redox center at the ab initio quantum chemistry level of theory and the protein reorganization with long-time MD simulations on the microsecond timescale. The calculations successfully evaluated a large absolute redox potential, 4.34 eV, with errors of only 0.03 to 0.34 eV to the experimental ones without any problem-specific empirical parameters. Through the long-time MD sampling, large and nonlinear reorganization of the protein environment was unveiled and the molecular determinants for the redox potential were identified. The present ab initio approach significantly expands the applicability of theoretical investigation to biological redox systems with more electronically complicated redox centers such as polynuclear transition metal complexes.

A Density Functional Theory-Based Scheme to Compute the Redox Potential of a Transition Metal Complex: Applications to Heme Compound

We estimated the redox potential of a model heme compound by using the combination of our density functionals with a computational scheme, which corrects the solvation energy to the normal solvent model. Among many density functionals, the LC-BOP12 functional gave the smallest mean absolute error of 0.16 V in the test molecular sets. The application of these methods revealed that the redox potential of a model heme can be controlled within 200 mV by changing the protonation state and even within 20 mV by the flipping of the ligand histidine. In addition, the redox potential depends on the inverse of the dielectric constant, which controls the surroundings. The computational results also imply that a system with a low dielectric constant avoids the charged molecule by controlling either the redox potential or the protonation system.

QM-Mechanism-Based Hierarchical High-Throughput in Silico Screening Catalyst Design for Ammonia Synthesis

We propose and test a hierarchical high-throughput screening (HHTS) approach to catalyst design for complex catalytic reaction systems that is based on quantum mechanics (QM) derived full reaction networks with QM rate constants but simplified to examine only the reaction steps likely to be rate determining. We illustrate this approach by applying it to determine the optimum dopants (our of 35 candidates) to improve the turnover frequency (TOF) for the Fe-based Haber-Bosch ammonia synthesis process. We start from the QM-based free-energy reaction network for this reaction over Fe(111), which contains the 26 most important surface configurations and 17 transition states at operating conditions of temperature and pressure, from which we select the key reaction steps that might become rate determining for the alloy. These are arranged hierarchically by decreasing free-energy reaction barriers. We then extract from the full reaction network, a reduced set of reaction rates required to quickly predict the effect of the catalyst changes on each barrier. This allows us to test new candidates with only 1% of the effort for a full calculation. Thus, we were able to quickly screen 34 candidate dopants to select a small subset (Rh, Pt, Pd, Cu) that satisfy all criteria, including stability. Then from these four candidates expected to increase the TOF for NH₃ production, we selected the best candidate (Rh) for a more complete free-energy and kinetic analysis (10 times the effort for HHTS but still 10% of the effort for a complete analysis of the full reaction network). We predict that Rh doping of Fe will increase the TOF for NH₃ synthesis by a factor of ∼3.3 times compared to Fe(111), in excellent agreement with our HHTS predictions, validating this approach.

Computational electrochemistry of a novel ferrocene derivative

In this study, the structural and redox properties of a novel ferrocene derivative in dichlomethane solvent were investigated. For this aim, various exchange-correlation functionals and basis sets in gas phase with different continuum solvation models and cavities in liquid phase were applied. The results indicated that UM06/6-31++G(d,p)/SDD level of theory successfully calculated bond lengths and angles with MADs = 0.02 Å and 0.78 deg., respectively. Also, its combination with CPCM-Pauling-UHF/6-31+G(d)/SDD level of theory in liquid phase effectively computed the redox potential with 0.06 V deviation from the experimental value. Moreover, transferability of the proposed method was studied through ferrocene molecule and its new synthesized derivative.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Homogeneously Catalyzed Electroreduction of Carbon Dioxide-Methods, Mechanisms, and Catalysts

The utilization of CO₂ via electrochemical reduction constitutes a promising approach toward production of value-added chemicals or fuels using intermittent renewable energy sources. For this purpose, molecular electrocatalysts are frequently studied and the recent progress both in tuning of the catalytic properties and in mechanistic understanding is truly remarkable. While in earlier years research efforts were focused on complexes with rare metal centers such as Re, Ru, and Pd, the focus has recently shifted toward earth-abundant transition metals such as Mn, Fe, Co, and Ni. By application of appropriate ligands, these metals have been rendered more than competitive for CO₂ reduction compared to the heavier homologues. In addition, the important roles of the second and outer coordination spheres in the catalytic processes have become apparent, and metal-ligand cooperativity has recently become a well-established tool for further tuning of the catalytic behavior. Surprising advances have also been made with very simple organocatalysts, although the mechanisms behind their reactivity are not yet entirely understood. Herein, the developments of the last three decades in electrocatalytic CO₂ reduction with homogeneous catalysts are reviewed. A discussion of the underlying mechanistic principles is included along with a treatment of the experimental and computational techniques for mechanistic studies and catalyst benchmarking. Important catalyst families are discussed in detail with regard to mechanistic aspects, and recent advances in the field are highlighted.

Electronic effect of ligands vs. reduction potentials of Fischer carbene complexes of chromium: a molecular electrostatic potential analysis

Molecular electrostatic potential at the chromium centre (V_Cr) emerges as a powerful predictor of reduction potential (E⁰).

Cyclopentadienone iron complexes as efficient and selective catalysts for the electroreduction of CO2 to CO

Robust and easy-to-synthesize cyclopentadienone iron(0) complexes selectively catalyze the electrochemical conversion of CO₂ to CO. Cooperation between the metal center and the coordinated organic ligand is a key factor for activity of these novel electrocatalysts.

A density functional theory protocol for the calculation of redox potentials of copper complexes

The calculated redox potentials of copper complexes agree nicely with their corresponding experimental redox potentials.

Successful application of the DBLOC method to the hydroxylation of camphor by cytochrome p450

The activation barrier for the hydroxylation of camphor by cytochrome P450 was computed using a mixed quantum mechanics/molecular mechanics (QM/MM) model of the full protein-ligand system and a fully QM calculation using a cluster model of the active site at the B3LYP/LACVP*/LACV3P** level of theory, which consisted of B3LYP/LACV3P** single point energies computed at B3LYP/LACVP* optimized geometries. From the QM/MM calculation, a barrier height of 17.5 kcal/mol was obtained, while the experimental value was known to be less than or equal to 10 kcal/mol. This process was repeated using the D3 correction for hybrid DFT in order to investigate whether the inadequate treatment of dispersion interaction was responsible for the overestimation of the barrier. While the D3 correction does reduce the computed barrier to 13.3 kcal/mol, it was still in disagreement with experiment. After application of a series of transition metal optimized localized orbital corrections (DBLOC) and without any refitting of parameters, the barrier was further reduced to 10.0 kcal/mol, which was consistent with the experimental results. The DBLOC method to CH bond activation in methane monooxygenase (MMO) was also applied, as a second, independent test. The barrier in MMO was known, by experiment, to be 15.4 kcal/mol. After application of the DBLOC corrections to the MMO barrier compute by B3LYP, in a previous study, and accounting for dispersion with Grimme's D3 method, the unsigned deviation from experiment was improved from 3.2 to 2.3 kcal/mol. These results suggested that the combination of dispersion plus localized orbital corrections could yield significant quantitative improvements in modeling the catalytic chemistry of transition-metal containing enzymes, within the limitations of the statistical errors of the model, which appear to be on the order of approximately 2 kcal/mole.

Trends in predicted chemoselectivity of cytochrome P450 oxidation: B3LYP barrier heights for epoxidation and hydroxylation reactions

Prediction of epoxide formation in drug metabolism is a difficult but important task, as epoxide formation is linked to drug toxicity. A comparison of the energy barriers for cytochrome P450 mediated epoxidation of alkenes to the barriers for the hydroxylation of an aliphatic carbon atom next to a double bond has been performed using B3LYP and B3LYP-D3. Relevant experimental data on oxidation selectivity has also been assessed. The results show that density functional theory, when using B3LYP-D3, does well in reproducing the experimental trends. Considering that the comparison involves chemical steps with quite different features this is remarkable. We also find that B3LYP consistently underestimates the hydrogen abstraction barriers relative to the epoxidation barriers, and that including a dispersion correction reduces this problem.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Applications of density functional theory to iron-containing molecules of bioinorganic interest

The past decades have seen an explosive growth in the application of density functional theory (DFT) methods to molecular systems that are of interest in a variety of scientific fields. Owing to its balanced accuracy and efficiency, DFT plays particularly useful roles in the theoretical investigation of large molecules. Even for biological molecules such as proteins, DFT finds application in the form of, e.g., hybrid quantum mechanics and molecular mechanics (QM/MM), in which DFT may be used as a QM method to describe a higher prioritized region in the system, while a MM force field may be used to describe remaining atoms. Iron-containing molecules are particularly important targets of DFT calculations. From the viewpoint of chemistry, this is mainly because iron is abundant on earth, iron plays powerful (and often enigmatic) roles in enzyme catalysis, and iron thus has the great potential for biomimetic catalysis of chemically difficult transformations. In this paper, we present a brief overview of several recent applications of DFT to iron-containing non-heme synthetic complexes, heme-type cytochrome P450 enzymes, and non-heme iron enzymes, all of which are of particular interest in the field of bioinorganic chemistry. Emphasis will be placed on our own work.

Accurate pKa prediction in first-row hexaaqua transition metal complexes using the B3LYP-DBLOC method

Acid dissociation constants are computed with density functional theory (DFT) for a series of ten first-row octahedral hexaaqua transition metal complexes at the B3LYP/LACV3P** level of theory. These results are then scaled, primarily to correct for basis set effects (as in previous work on predicting pKa's in organic systems1-5). Finally, localized orbital corrections (LOCs), developed by fitting properties such as ionization potentials, electron affinities, and ligand removal energies in prior publications,3,4,6,7 are applied without any further parameter adjustment. The combination of a single scale factor with the DBLOC (localized orbital corrections for first row transition metals) corrections (and thus a single adjustable parameter in all) improves the mean unsigned error from 5.7 pKa units (with no parameters) to 0.9 pKa units (maximum error 2.2 pKa units), which is close to chemical accuracy for this type of system. These results provide further encouragement with regard to the ability of the B3LYP-DBLOC model to provide accurate and robust results for DFT calculations on transition metal containing species.

What can density functional theory tell us about artificial catalytic water splitting?

Water splitting by artificial catalysts is a critical process in the production of hydrogen gas as an alternative fuel. In this paper, we examine the essential role of theoretical calculations, with particular focus on density functional theory (DFT), in understanding the water-splitting reaction on these catalysts. First, we present an overview of DFT thermochemical calculations on water-splitting catalysts, addressing how these calculations are adapted to condensed phases and room temperature. We show how DFT-derived chemical descriptors of reactivity can be surprisingly good estimators for reactive trends in water-splitting catalysts. Using this concept, we recover trends for bulk catalysts using simple model complexes for at least the first-row transition-metal oxides. Then, using the CoPi cobalt oxide catalyst as a case study, we examine the usefulness of simulation for predicting the kinetics of water splitting. We demonstrate that the appropriate treatment of solvent effects is critical for computing accurate redox potentials with DFT, which, in turn, determine the rate-limiting steps and electrochemical overpotentials. Finally, we examine the ability of DFT to predict mechanism, using ruthenium complexes as a focal point for discussion. Our discussion is intended to provide an overview of the current strengths and weaknesses of the state-of-the-art DFT methodologies for condensed-phase molecular simulation involving transition metals and also to guide future experiments and computations toward the understanding and development of novel water-splitting catalysts.

Covalent O-H bonds as electron traps in proton-rich rutile TiO2 nanoparticles

The cation in the electrolyte of the dye-sensitized solar cell (DSSC) has a profound effect on electron trapping and transport behavior in TiO2 nanocrystalline film; this is one of the important factors that determines the overall efficiency of DSSCs. Here, we present a quantum mechanical investigation on the structures and energetics of proton-induced electron trap states and the thermodynamical barrier heights for the ambipolar diffusion of proton/electron pair using a large cluster model for the computations. Our calculations indicate that protons react with TiO2 to form covalent O-H bonds. This is in contrast to the reaction of Li(+) with TiO2, in which case the alkali metal is more accurately described as a simple coordinating cation. The covalent O-H bonding leads both to deeper electron trap states and to significantly higher barriers for the diffusion of carriers. These results are qualitatively consistent with experimental observations, and they extend our understanding of the cation effect in DSSCs at an atomic level of detail.

Quantum mechanical methods for the investigation of metalloproteins and related bioinorganic compounds

It is well known that transition metal ions are often bound to proteins, conveying very specific functional properties. In fact, metalloproteins play crucial biological roles in the transport and activation of small molecules such as H2, O2, and N2, as well as in several other biochemical processes. However, even if the presence of transition metals in the active site of proteins allows a very rich biochemistry, the experimental disclosure of structure-activity relationships in metalloproteins is generally difficult exactly because of the presence of transition metals, which are intrinsically characterized by a very versatile and often elusive chemistry. For this reason, computational methods are becoming very popular tools in the characterization of metalloproteins. In particular, since computing power is becoming less and less expensive, due to the continuous technological development of CPUs, the computational tools suited to investigate metalloproteins are becoming more accessible and therefore more commonly used also in molecular biology and biochemistry laboratories. Here, we present the main procedures and computational methods based on quantum mechanics, which are commonly used to study the structural, electronic, and reactivity properties of metalloproteins and related bioinspired compounds, with a specific focus on the practical and technical aspects that must be generally tackled to properly study such biomolecular systems.

Rational design of Co-based redox mediators for dye-sensitized solar cells by density functional theory

We theoretically describe the effects of chemically modifying polypyridine ligands and design efficient Co-based redox mediators for dye-sensitized solar cells.

Computational approaches to the chemical conversion of carbon dioxide

The conversion of CO₂ into fuels and chemicals is viewed as an attractive route for controlling the atmospheric concentration and recycling of this greenhouse gas, but its industrial application is limited by the low selectivity and activity of the current catalysts. Theoretical modeling, in particular density functional theory (DFT) simulations, provides a powerful and effective tool to discover chemical reaction mechanisms and design new catalysts for the chemical conversion of CO₂, overcoming the repetitious and time/labor consuming trial-and-error experimental processes. In this article we give a comprehensive survey of recent advances on mechanism determination by DFT calculations for the catalytic hydrogenation of CO₂ into CO, CH₄, CH₃OH, and HCOOH, and CO₂ methanation, as well as the photo- and electrochemical reduction of CO₂. DFT-guided design procedures of new catalytic systems are also reviewed, and challenges and perspectives in this field are outlined.