Transition Metals in Coordination Environments

Spin crossover (SCO) plays a vital role in living systems and in many emerging technologies, and the accurate prediction and design of SCO systems is of high current priority. Density functional theory (DFT) is the state-of-the-art tool for this purpose due to its ability to describe large molecular electronic systems with an accuracy that can be predictive if carried out correctly. However, the SCO tendency, i.e., the free-energy balance of high- and low-spin states, is extremely sensitive to the theoretical description and physical effects such as dispersion, relativistic effects, and vibrational entropy. This chapter summarizes the recent fundamental insight into SCO gained from DFT and efforts that approach the accuracy needed (~10 kJ/mol) for rational design of SCO to become reality.

Spectroscopic investigations of the interaction of a spin magnetic moment with an external magnetic field reveal insight into the electronic structure, e.g. the composition of the occupied molecular orbitals of the system, the oxidation state of a possible transition metal and its coordination environment. For paramagnetic systems, electron spin resonance (ESR) and related techniques probe the interaction between electron and nuclear spins, provide information about the spatial distribution of the spin density and allow identifying binding partners which are often not resolved structurally, for example hydrogen atoms. In particular, diagonalization of the electron Zeeman and electron-nuclear hyperfine interaction matrices does not only give their principal values but also their magnetic principal axes and allows making statements about the spatial arrangement of coordinating atoms and ligands. The advancement of computational approaches to calculate the parameters of the effective Spin Hamiltonian such as the electronic g-tensors and hyperfine tensors and their comparison with experiment supports the analysis and interpretation of complex magnetic resonance spectra. This is discussed here for g- and hyperfine tensors and zero-field splitting tensors for selected examples including transition metal containing model complexes and metalloenzymes.

Chemical bonding in transition metal complexes is typically described by Dewar–Chatt–Duncanson model which separates donation (ligand → metal) and back-donation (metal → ligand) charge transfer processes—these are with no doubt crucial factors which determine a number of properties of metal complexes. This contribution highlights the importance of various non-covalent interactions including untypical homopolar dihydrogen contacts C–H•••H–C in metal complexes. The selected systems are: (1) Zn(II) species containing NTA (nitrotriacetic acid), NTPA (nitrotri-3-propanoic), BPy (2,2′-bipyridyl) ligands, (2) cis-NiL₂–hexane (L–thiourea-based ligand) complex, and (3) hydrogen storage materials LiNMe₂BH₃ and KNMe₂BH₃. It is shown consistently by various methods and bonding descriptors including for example the charge and energy decomposition scheme ETS-NOCV, Interacting Quantum Atoms (IQA), Reduced Density Gradient (NCI), Quantum Theory of Atoms in Molecules (QTAIM) and NMR spin-spin ¹J(C–H) coupling constants, that London dispersion dominated C–H•••H–C interactions and other more typical hydrogen bonds (e.g. C–H•••N, C–H•••O) driven mostly by electrostatics, are crucial for determination of the structures and stability of the selected metal complexes. Although London dispersion forces are the fundamental factor (~70% of the overall stabilization) contributing to C–H•••H–C interactions, the charge delocalization (outflow of electrons from the σ(C–H) bonds engaged in C–H•••H–C and the accumulation in the interatomic H•••H region) as well as electrostatic terms are also non-negligible (~30%). Remarkably, hydride–hydride interactions B–H•••H–B in LiNMe₂BH₃ are found to be repulsive due to dominant destabilizing electrostatic contribution as opposed to stabilizing C–H•••H–C.

Transition metal complexes containing magnetically interacting open-shell ions are important for diverse areas of molecular science. The reliable prediction and computational analysis of their electronic structure and magnetic properties, either in qualitative or quantitative terms, remain a central challenge for theoretical chemistry. The use of multireference methods is in principle the ideal approach to the inherently multireference problem of exchange coupling in oligonuclear transition metal complexes; however, the applicability of such methods has been severely restricted due to their computational cost. In recent years, the introduction of the density matrix renormalization group (DMRG) to quantum chemistry has enabled the multireference treatment of chemical problems with previously unattainable numbers of active electrons and orbitals. This development also paved the way for the first-principles multireference treatment of magnetic properties in the case of exchange-coupled transition metal systems. Here, the first detailed applications of DMRG-based methods to exchange-coupled systems are reviewed and the lessons learned so far regarding the applicability, apparent limitations, and future promise of this approach are discussed.

This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic Hamiltonians that are frequently applied to account for relativistic effects. Then, we scrutinize various quantum chemistry methods that approximate the N-electron wave function. In this respect, we will review the most popular single- and multi-reference approaches that have been developed to model the multi-reference nature of heavy element compounds and their ground- and excited-state electronic structures. Specifically, we introduce various flavors of post-Hartree–Fock methods and optimization schemes like the complete active space self-consistent field method, the configuration interaction approach, the Fock-space coupled cluster model, the pair-coupled cluster doubles ansatz, also known as the antisymmetric product of 1 reference orbital geminal, and the density matrix renormalization group algorithm. Furthermore, we will illustrate how concepts of quantum information theory provide us with a qualitative understanding of complex electronic structures using the picture of interacting orbitals. While modern quantum chemistry facilitates a quantitative description of atoms and molecules as well as their properties, concepts of quantum information theory offer new strategies for a qualitative interpretation that can shed new light onto the chemistry of complex molecular compounds.

Knowledge of the electronic structure of transition-metal complexes is increasingly being obtained through joint efforts by theory and experiments. Here, we describe a variety of examples where spectroscopy is being used to determine, e.g., the oxidation state, spin state, or coordination environment around redox-active metal ions such as iron, manganese, or nickel. Both enzymatic and biomimetic systems are included, from the literature and from our own laboratories. It is shown that the combined efforts of wet and dry laboratories lead to a more profound understanding, and allows for systematic exploration of coordinate chemistry around the central metal atom.

Close correlation between theoretical modeling and experimental spectroscopy allows for identification of the electronic and geometric structure of a system through its spectral fingerprint. This is can be used to verify mechanistic proposals and is a valuable complement to calculations of reaction mechanisms using the total energy as the main criterion. For transition metal systems, X-ray spectroscopy offers a unique probe because the core-excitation energies are element specific, which makes it possible to focus on the catalytic metal. The core hole is atom-centered and sensitive to the local changes in the electronic structure, making it useful for redox active catalysts. The possibility to do time-resolved experiments also allows for rapid detection of metastable intermediates. Reliable fingerprinting requires a theoretical model that is accurate enough to distinguish between different species and multiconfigurational wavefunction approaches have recently been extended to model a number of X-ray processes of transition metal complexes. Compared to ground-state calculations, modeling of X-ray spectra is complicated by the presence of the core hole, which typically leads to multiple open shells and large effects of spin–orbit coupling. This chapter describes how these effects can be accounted for with a multiconfigurational approach and outline the basic principles and performance. It is also shown how a detailed analysis of experimental spectra can be used to extract additional information about the electronic structure.

In the field of B\(_{12}\) chemistry, absorption spectroscopy, hand in hand with computational modeling, has played an important role in describing electronically excited states of vitamin B\(_{12}\) derivatives, also known as cobalamins. This chapter focuses on the current understanding of absorption properties of cobalamins from both spectroscopic and computational points of views. The main emphasis is on methylcobalamin (MeCbl), adenosylcobalamin (AdoCbl), and cyanocobalamin (CNCbl). In addition, we will discuss some other unique derivatives including antivitamins, non-alkyl cobalamins, as well as reduced and super-reduced forms. Due to the complexity and the size of these systems, computational analysis is almost exclusively represented by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. Proper DFT functional choice is paramount in predicting electronic transitions and simulating the full spectrum reliably. At this juncture in the field of B\(_{12}\) chemistry, it is indisputable that the BP86 functional is the proper choice for the assessment of the electronically excited states of cobalamins.

A detailed molecular-level understanding of the excited-state (ES) decay dynamics of transition metal complexes (TMCs) is vital to develop the next generation of light-active components in a wide variety of applications related to photochemistry, including optoelectronics, photocatalysis, dye-sensitized solar cells, artificial photosynthesis, photonics sensors and switches, and bioimaging. After photoexcitation, TMCs can undergo a plethora of interconnected relaxation processes, which compete to each other and are controlled by the subtle interplay of electronic and geometrical rearrangements that take place during the ES deactivation dynamics at different timescales. Intrinsic factors such as (i) the spin and character of the electronically ES involved in the process and (ii) the energetic alignment and effective couplings between these states do play a protagonist role in determining the preferred deactivation channels. Extrinsic factors, such as temperature, pressure, excitation wavelength, and environmental effects, can often strongly modify the outcome of the photochemical processes. As kinetic control is always at play, only the fastest processes among all possible deactivation channels are generally observed. Due to their high density of ES of various characters, TMCs usually display rich and chameleonic ES and photochemical properties. Computational chemistry is a powerful and unique tool to provide a microscopic and time-resolved description of these complex processes, and it often constitutes the fundamental ingredient for the interpretation of time-resolved absorption and emission spectroscopic measurements. This chapter provides first a general overview on this complex topic, followed by an overview of the state-of-the-art quantum chemical and reaction dynamics methods to study the photodeactivation dynamics of TMCs and finally illustrates the progress and challenges in this field with recent examples from the literature. Importantly, these examples cover the ultrafast ES decay regime but also the long-lived photodeactivation from thermally equilibrated ES.

The use of computational methods based on electronic structure theory and statistical mechanics to study reaction mechanisms and kinetics in homogeneous catalysis, especially organometallic catalysis and organocatalysis, is reviewed. The chapter focuses mostly on examples from the authors’ own group, published over the last two decades, and discusses progress and remaining challenges. It is argued that while it plays a valuable role in mechanistic studies, computation is not yet able to replace experimental studies.

Chromium, molybdenum and tungsten oxides supported on amorphous silica are catalysts for many reactions, including large-scale industrial processes. Although these systems have been extensively studied for many years, there are still a few unresolved issues, concerning mainly the nature of the active sites and mechanisms of their formation. Computational studies, using cluster or periodic models to represent the catalyst surface, are helpful in interpretation of spectroscopic data and can provide complementary information about the catalytic process. In this chapter, such computational works on CrO_x/SiO₂, MoO_x/SiO₂ and WO_x/SiO₂ systems are presented. It is seen that coordination environment of the transition metal, determined also by local surface properties, is a key factor influencing catalytic activity of the surface metal species. This results in complex structure–activity relationships. While a great progress has been achieved in modelling of these systems, from simple clusters to advanced periodic slabs, theoretical determination of complex reaction mechanisms using surface models with representative distribution of metal sites is still a challenge for computational catalysis.

This chapter is the review of the computational methods applied to the transition metal oxides most abundant in heterogeneous catalysis and is focused on the influence of the environment on the transition metal cation properties. The shortcomings of the most commonly used DFT level of theory are discussed, and its extensions towards more realistic environment are presented. The modern reactive force-field methods are also mentioned. The embedding schemes most commonly found in the quantum-chemical or classical description of the heterogeneous processes are discussed. The errors stemming from the non-completeness of the basis function, i.e. the basis set superposition error, found in the calculations with atomic basis, and the Pulay stress, occurring in the planewave calculations, together with remedies, are briefly described. It is shown that in all discussed systems, i.e. \( {\mathrm {CeO}}_{2}\), \({\mathrm {TiO}}_{2}\), \({\mathrm {ZrO}}_{2}\), zeolites, d-electron metal spinels, and \({\mathrm {V}}_{2}\mathrm{O}_{5}\), the appropriately applied Hubbard DFT GGA+U methods are successful for the compromise between computational cost and resultant accuracy. The much more time-consuming hybrid functionals give slightly more accurate results and, moreover, are more universal in the sense that they do not need calibration against experiment contrary to DFT+U where the Hubbard correction needs to be carefully selected for modelling particular properties.

This contribution shows how molecular electrochemistry may benefit from the application of DFT methods combined with implicit solvent models. The progress in quantum chemical calculations, including efficient solvation models, has brought about the development of effective computational protocols that allow accurate (to 0.05 V) reproduction of experimental redox potentials of mono- and dinuclear complexes, including electrocatalytically relevant systems and mixed-valence compounds. These calculations may also help to understand how electronic and structural factors, modulated by the changes in both first and second coordination spheres, and the local environment (dielectric medium and specific interactions), govern the ability of transition metal complexes to undergo electron transfer (ET) processes. Understanding the principles that lie behind it is of great importance in redox chemistry and catalysis, and biological systems. After a brief introduction to modelling approaches and discussion of challenges for calibration of computational protocols based on comparison with experimental data, a number of noteworthy case studies are given. Specifically, the determination of ferrocenium/ferrocene absolute potentials in solvents commonly used in electrochemistry is discussed, the redox behaviour of Cu and Fe systems affected by H-bonding, followed by the presentation of intriguing properties of mono- and bimetallic Mo/W scorpionates. Particularly, electrochemical communication between metal centres and a baffling (auto)catalytic dehalogenation triggered by ET through a C−H⋯O_alkoxide hydrogen bond, the mechanism of which was unravelled owing to the application of dispersion-corrected DFT calculations, are highlighted.

Enzymes are versatile oxidants in Nature that catalyze a range of reactions very efficiently. Experimental studies on the mechanism of enzymes are sometimes difficult due to the short lifetime of catalytic cycle intermediates. Theoretical modeling can assist and guide experiment and elucidate mechanisms for fast reaction pathways. Two key computational approaches are in the literature, namely quantum mechanics/molecular mechanics (QM/MM) on complete enzyme structures and QM cluster models on active site structures only. These two approaches are reviewed here. We give examples where the QM cluster approach worked well and, for instance, enabled the bioengineering of an enzyme to change its functionality. In addition, several examples are given, where QM cluster models were insufficient and full QM/MM structures were needed to establish regio-, chemo-, and stereoselectivities.

The chemistry of transition-metal-containing systems is highly complex and diverse and thus lends itself to careful computational investigation. Indeed, computational chemistry can play fundamentally important roles in elucidating the catalytic mechanisms of such systems, by offering information about short-lived intermediates and transition states as well as factors that determine catalytic properties, which is not easily attained by experimental means. A quantum mechanical description of a targeted catalytic system could be difficult or unfeasible in many circumstances, especially when large systems such as metalloenzymes and coordination polymers are studied. Nevertheless, valuable insights can still be gained from hybrid computational techniques that allow concrete realizations of extensive reaction pathway analyses. This chapter gives a brief overview of some of our recent attempts to study the structure and activity of transition-metal-containing systems varying in size using several computational approaches.

Methanol dehydrogenase (MDH) enzymes are quinoproteins that require calcium or magnesium ion as well as pyrroloquinoline quinone as a cofactor for activity in the oxidation of methanol to formaldehyde. Lately, MDH enzymes containing lanthanide ions in the active site have been isolated in drastic conditions from Methylacidiphilum fumariolicum bacterium. The present theoretical study performed in the framework of the density functional theory employing the quantum mechanical cluster approach mainly focused on the catalytic mechanism of cerium containing MDH enzyme. In order to rationalize the effect of the metal ion substitution on the catalytic activity, geometrical and electronic properties of the “Michaelis–Menten” enzyme–methanol complexes of Ce-MDH and Eu-MDH are also discussed as well as the substrate’s activation mediated by the metal ion. With the aim to better describe the Lewis acidity of metal ions in the methanol oxidation, the comparison of the catalytic performance between Ce-MDH and Ca-MDH was also made.

Modelling structure and/or reaction mechanism of a metalloenzyme requires constructing reliable computational models. This process usually starts with crystal structure and involves several steps, each potentially influencing the accuracy of the constructed model. In this chapter, we provide an account, from our own works and from the literature, on how one can check the quality of the crystal structure, predict protonation states of titratable residues, including the metal ligands, perform molecular dynamics simulations, chose representative snapshots, and finally, construct a QM cluster model that can be used for mechanistic studies.