Ironing out the photochemical and spin-crossover behavior of Fe(II) coordination compounds with computational chemistry

Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Recent transformative advances in computing power and algorithms have made computational chemistry central to the discovery and design of new molecules and materials. First-principles simulations are increasingly accurate and applicable to large systems with the speed needed for high-throughput computational screening. Despite these strides, the combinatorial challenges associated with the vastness of chemical space mean that more than just fast and accurate computational tools are needed for accelerated chemical discovery. In transition-metal chemistry and catalysis, unique challenges arise. The variable spin, oxidation state, and coordination environments favored by elements with well-localized d or f electrons provide great opportunity for tailoring properties in catalytic or functional (e.g., magnetic) materials but also add layers of uncertainty to any design strategy. We outline five key mandates for realizing computationally driven accelerated discovery in inorganic chemistry: (i) fully automated simulation of new compounds, (ii) knowledge of prediction sensitivity or accuracy, (iii) faster-than-fast property prediction methods, (iv) maps for rapid chemical space traversal, and (v) a means to reveal design rules on the kilocompound scale. Through case studies in open-shell transition-metal chemistry, we describe how advances in methodology and software in each of these areas bring about new chemical insights. We conclude with our outlook on the next steps in this process toward realizing fully autonomous discovery in inorganic chemistry using computational chemistry.

High-temperature Spin Crossover of a Solvent-Free Iron(II) Complex with the Linear Hexadentate Ligand [Fe(L2-3-2Ph)](AsF6)2 (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3- propanediamine)

A novel mononuclear iron(II) complex with a linear hexadentate N6 ligand, containing two 1,2,3-triazole moieties, [Fe(L2-3-2Ph)](AsF6)2 (1), was synthesized (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3-propanediamine). Variable-temperature magnetic susceptibility measurements revealed a gradual one-step spin crossover (SCO) between the high-spin (HS, S = 2) and low-spin (LS, S = 0) states above room temperature (T1/2 = 468 K). The spin transition was further confirmed by differential scanning calorimetry (DSC). A single-crystal X-ray diffraction study showed that the complex was in the LS state (S = 0) at room temperature (296 K). In the crystal lattice, a three-dimensional (3D) supramolecular network was formed by intermolecular CH⋯ and – interactions of neighboring complex cations [Fe(L2-3-2Ph)]2+. AsF6− ions were located interstitially in the 3D network of complex cations, with no solvent-accessible voids. The crystal structure at 448 K (mixture of HS and LS species) was also successfully determined thanks to the thermal stability of the solvent-free crystal.

Designing air-stable cyclometalated Fe(ii) complexes: stabilization via electrostatic effects

Substitution of EWGs onto the cyclometelated iron complexes electrostatically stabilizes the Fe(ii) center while still preserving the increased ligand field strength.

Field-induced slow magnetic relaxation in pseudooctahedral cobalt(ii) complexes with positive axial and large rhombic anisotropy

The preparation, X-ray crystal structure, spectroscopic and variable-temperature dc and ac magnetic properties of two six-coordinate cobalt(ii) complexes of formula [Co(bim)₄(tcm)₂] (1) and [Co(bmim)₄(tcm)₂] (2) are reported.

Opto-Spintronics: Photoisomerization-Induced Spin State Switching at 300 K in Photochrome Cobalt-Dioxolene Thin Films

Controllable quantum systems are under active investigation for quantum computing, secure information processing, and nonvolatile memory. The optical manipulation of spin quantum states provides an important strategy for quantum control with both temporal and spatial resolution. Challenges in increasing the lifetime of photoinduced magnetic states at T > 200 K have hindered progress toward utilizing photomagnetic materials in quantum device architectures. Here we demonstrate reversible light-induced magnetization switching in an organic thin film at device operating temperatures of 300-330 K. By utilizing photochromic ligands that undergo structural changes in the solid state, the changes in ligand field associated with photoisomerization modulate the ligand field and in turn the oxidation and spin state of a bound metal center. Green light irradiation (λ_exc = 550 nm) of a spirooxazine cobalt-dioxolene complex induces photoisomerization of the ligand that in turn triggers a reversible intramolecular charge-transfer coupled spin-transition process at the cobalt center. The generation of photomagnetic states through conversion between a low-spin Co(III)-semiquinone doublet and a high-spin Co(II)-bis-semiquinone sextet state has been demonstrated in both solution and the solid state and is described as a photoisomerization-induced spin-charge excited state (PISCES) process. The high transition temperature (325 K) and long-lived photoinduced state (τ = 10 s at 300 K) are dictated by the photochromic ligand. Theory provides effective modeling of the phenomenon and long-term strategies to further modulate the lifetimes of photomagnetic states for quantum information technologies at the single molecule level.

Photoactive Complexes with Earth-Abundant Metals

In this invited Perspective, recent developments and possible future directions of research on photoactive coordination compounds made from nonprecious transition metal elements will be discussed. The focus is on conceptually new, structurally well-characterized complexes with excited-state lifetimes between 10 ps and 1 ms in fluid solution for possible applications in photosensitizing, light-harvesting, luminescence and catalysis. The key metal elements considered herein are Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Mo, W and Ce in various oxidation states equipped with diverse ligands, giving access to long-lived excited states via a range of fundamentally different types of electronic transitions. Research performed in this area over the past five years demonstrated that a much broader spectrum of metal complexes than what was long considered relevant exhibits useful photophysics and photochemistry.

Tuning the Redox Potentials and Ligand Field Strength of Fe(II) Polypyridines: The Dual π-Donor and π-Acceptor Character of Bipyridine

The quintet-singlet energy difference (Δ E_Q/S) in Fe(II) polypyridine complexes is often interpreted in terms of metal-ligand π interactions. DFT calculations on a series of substituted [Fe(bpy)₃]²⁺ (bpy = 2,2'-bipyridine) complexes show the disparate magnitudes of substituent effects on tuning Δ E_Q/S and reduction potentials ( E°). In this series, E° spans a much larger range than Δ E_Q/S (2.07 vs 0.29 eV). While small changes in Δ E_Q/S are controlled by metal-ligand π interactions, large changes in E° arise from modification of the electrostatic environment around the Fe center. Molecular orbital analysis reveals that, contrary to the typical description of bpy as a π-acceptor, bpy is better described as acting as both a π-donor and π-acceptor in [Fe(bpy)₃]²⁺ complexes, even when it is substituted with highly electron withdrawing substituents. Overall, substituent modification is a useful strategy for fine-tuning the ligand field strength but not for significant reordering of the spin-state manifold, despite the large effect on metal-ligand electrostatic interactions.

Synthesis and Computational Study of a Pyridylcarbene Fe(II) Complex: Unexpected Effects of fac/ mer Isomerism in Metal-to-Ligand Triplet Potential Energy Surfaces

The synthesis and the steady-state absorption spectrum of a new pyridine-imidazolylidene Fe(II) complex (Fe-NHC) are presented. A detailed mechanism of the triplet metal-to-ligand charge-transfer states decay is provided on the basis of minimum energy path (MEP) calculations used to connect the lowest-lying singlet, triplet, and quintet state minima. The competition between the different decay pathways involved in the photoresponse is assessed by analyzing the shapes of the obtained potential energy surfaces. A qualitative difference between facial ( fac) and meridional ( mer) isomers' potential energy surface (PES) topologies is evidenced for the first time in iron-based complexes. Indeed, the mer complex shows a steeper triplet path toward the corresponding ³MC minimum, which lies at a lower energy as compared to the fac isomer, thus pointing to a faster triplet decay of the former. Furthermore, while a major role of the metal-centered quintet state population from the triplet ³MC region is excluded, we identify the enlargement of iron-nitrogen bonds as the main normal modes driving the excited-state decay.

Bidirectional Photoswitching via Alternating NIR and UV Irradiation on a Core-Shell UCNP-SCO Nanosphere

Bidirectional photoswitching of molecular materials under ambient condition is of significant importance. Herein, we present for the first time that a core-shell UCNP-SCO nanosphere (UCNP = upconversion nanophosphor, SCO = spin crossover), which was composed of a UCNP core (NaYF₄: 20 mol % Yb³⁺, 1 mol % Er³⁺) and an SCO iron(II) shell ([Fe(H₂Bpz)₂(bipy-COOH)], H₂Bpz = dihydrobis(1-pyrazolyl)borate, bipy-COOH = 4,4'-dicarboxy-2,2'-bipyridine), can be reversibly photoswitched between the high-spin and low-spin states at room temperature in the solid state, via alternating irradiation with near-infrared (λ = 980 nm) and ultraviolet (λ = 310 nm) light. What's more, this reversible spin-state switching was accompanied by a variation of fluorescent spectrum and dielectric constants. The strategy here, that is, integrating the SCO iron(II) complex into a UCNP-SCO nanosphere for molecular photoswitching, may open a new area in the development of photocontrolled molecular devices.

A flexible, redox-active macrocycle enables the electrocatalytic reduction of nitrate to ammonia by a cobalt complex

Mechanistic investigations into electrocatalytic nitrate reduction by a cobalt complex reveal the critical role played by the flexible, redox-active ligand.

The cobalt macrocycle complex [Co(DIM)Br₂]⁺ (DIM = 2,3-dimethyl-1,4,8,11-tetraazacyclotetradeca-1,3-diene) is an electrocatalyst for the selective reduction of nitrate to ammonia in aqueous solution. The catalyst operates over a wide pH range and with very high faradaic efficiency, albeit with large overpotential. Experimental investigations, supported by electronic structure calculations, reveal that catalysis commences when nitrate binds to the two-electron reduced species Co^II(DIM^–), where cobalt and the macrocycle are each reduced by a single electron. Several mechanisms for the initial reduction of nitrate to nitrite were explored computationally and found to be feasible at room temperature. The reduced DIM ligand plays an important role in these mechanisms by directly transferring a single electron to the bound nitrate substrate, activating it for further reactions. These studies further reveal that the DIM macrocycle is critical to nitrate reduction, specifically its combination of redox non-innocence, hydrogen-bonding functionality and flexibility in coordination mode.

Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes

The accurate calculation of ligand dissociation (or equivalently, ligand binding) energies is crucial for computational coordination chemistry. Despite its importance, obtaining accurate ab initio reference data is difficult, and density-functional methods of uncertain reliability are chosen for feasibility reasons. Here, we consider advanced coupled-cluster and multiconfigurational approaches to reinvestigate our WCCR10 set of 10 gas-phase ligand dissociation energies [ J. Chem. Theory Comput. 2014, 10, 3092]. We assess the potential multiconfigurational character of all molecules involved in these reactions with a multireference diagnostic [ Mol. Phys. 2017, 115, 2110] in order to determine where single-reference coupled-cluster approaches can be applied. For some reactions of the WCCR10 set, large deviations of density-functional results including semiclassical dispersion corrections from experimental reference data had been observed. This puzzling observation deserves special attention here, and we tackle the issue (i) by comparing to ab initio data that comprise dispersion effects on a rigorous first-principles footing and (ii) by a comparison of density-functional approaches that model dispersion interactions in various ways. For two reactions, species exhibiting nonnegligible static electron correlation were identified. These two reactions represent hard problems for electronic structure methods and also for multireference perturbation theories. However, most of the ligand dissociation reactions in WCCR10 do not exhibit static electron correlation effects, and hence, we may choose standard single-reference coupled-cluster approaches to compare with density-functional methods. For WCCR10, the Minnesota M06-L functional yielded the smallest mean absolute deviation of 13.2 kJ mol^-1 out of all density functionals considered (PBE, BP86, BLYP, TPSS, M06-L, PBE0, B3LYP, TPSSh, and M06-2X) without additional dispersion corrections in comparison to the coupled-cluster results, and the PBE0-D3 functional produced the overall smallest mean absolute deviation of 4.3 kJ mol^-1. The agreement of density-functional results with coupled-cluster data increases significantly upon inclusion of any type of dispersion correction. It is important to emphasize that different density-functional schemes available for this purpose perform equally well. The coupled-cluster dissociation energies, however, deviate from experimental results on average by 30.3 kJ mol^-1. Possible reasons for these deviations are discussed.

Toward Highly Accurate Spin State Energetics in First-Row Transition Metal Complexes: A Combined CASPT2/CC Approach

In previous work on the performance of multiconfigurational second-order perturbation theory (CASPT2) in describing spin state energetics in first-row transition metal systems [ Pierloot et al. J. Chem. Theory Comput. 2017 , 13 , 537 - 553 ], we showed that standard CASPT2 works well for valence correlation but does not describe the metal semicore (3s3p) correlation effects accurately. This failure is partially responsible for the well-known bias toward high-spin states of CASPT2. In this paper, we expand our previous work and show that this bias could be partly removed with a combined CASPT2/CC approach: using high-quality CASPT2 with extensive correlation-consistent basis sets for valence correlation and low-cost CCSD(T) calculations with minimal basis sets for the metal semicore (3s3p) correlation effects. We demonstrate that this approach is efficient by studying the spin state energetics of a series of iron complexes modeling important intermediates in oxidative catalytic processes in chemistry and biochemistry. On the basis of a comparison with bare CCSD(T) results from this and previous work, the average error of the CASPT2/CC approach is estimated at around 2 kcal mol^-1 in favor of high spin states.

Accelerating Chemical Discovery with Machine Learning: Simulated Evolution of Spin Crossover Complexes with an Artificial Neural Network

Machine learning (ML) has emerged as a powerful complement to simulation for materials discovery by reducing time for evaluation of energies and properties at accuracy competitive with first-principles methods. We use genetic algorithm (GA) optimization to discover unconventional spin-crossover complexes in combination with efficient scoring from an artificial neural network (ANN) that predicts spin-state splitting of inorganic complexes. We explore a compound space of over 5600 candidate materials derived from eight metal/oxidation state combinations and a 32-ligand pool. We introduce a strategy for error-aware ML-driven discovery by limiting how far the GA travels away from the nearest ANN training points while maximizing property (i.e., spin-splitting) fitness, leading to discovery of 80% of the leads from full chemical space enumeration. Over a 51-complex subset, average unsigned errors (4.5 kcal/mol) are close to the ANN's baseline 3 kcal/mol error. By obtaining leads from the trained ANN within seconds rather than days from a DFT-driven GA, this strategy demonstrates the power of ML for accelerating inorganic material discovery.

Luminescent complexes made from chelating isocyanide ligands and earth-abundant metals

In this invited frontier article, recently discovered d⁶ and d¹⁰ complexes with long-lived metal-to-ligand charge transfer (MLCT) excited states are highlighted. Chelating diisocyanide ligands give access to emissive Mo(0) and Cr(0) complexes with d⁶ electron configuration exhibiting photophysical properties similar to those of Ru(ii) polypyridines or cyclometalated Ir(iii) complexes. With Ni(0), these ligands yield luminescent tetrahedral d¹⁰ complexes similar to isoelectronic Cu(i) bis(diimine) compounds.

Resolving Transition Metal Chemical Space: Feature Selection for Machine Learning and Structure-Property Relationships

Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships of the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20× higher errors for feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5× smaller than the full RAC set produce sub- to 1 kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 Å MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.

HOMO inversion as a strategy for improving the light-absorption properties of Fe(ii) chromophores

Substitution of π-conjugated donor groups onto the polypyridine ligands in Fe(ii) complexes inverts the HOMO character and improves the light-absorption.

A computational study of a series of [Fe(tpy)₂]²⁺ (tpy = 2,2′:6′,2′′-terpyridine) complexes is reported, where the tpy ligand is substituted at the 4, 4′, and 4′′ positions by electron donor (furan, thiophene, selenophene, NH₂) and acceptor (carboxylic acid, NO₂) groups. Using DFT and TD-DFT calculations, we show that the substitution of heterocyclic π donor groups onto the tpy ligand scaffold leads to marked improvement of the [Fe(tpy)₂]²⁺ absorption properties, characterized by increased molar extinction coefficients, shift of absorption energies to longer wavelengths, and broadening of the absorption spectrum in the visible region. The observed changes in the light absorption properties are due to destabilization of ligand-centered occupied π orbital energies, thus increasing the interactions between the metal t_2g (HOMO) and ligand π orbitals. Substitution of extended π-conjugated groups, such as thienothiophene and dithienothiophene, further destabilizes the ligand π orbital energies, resulting in a fully ligand-localized HOMO (i.e., HOMO inversion) and additional improvement of the light absorption properties. These results open up a new strategy to tuning the light absorption properties of Fe(ii)-polypyridines.

Chromium complexes for luminescence, solar cells, photoredox catalysis, upconversion, and phototriggered NO release

Cr(iii) and Cr(0) complexes are earth-abundant alternatives to photosensitizers that are commonly made from precious metals.

Some complexes of Cr(iii) and Cr(0) have long been known to exhibit interesting photophysical and photochemical properties, but in the past few years important conceptual progress was made. This Perspective focuses on the recent developments of Cr(iii) complexes as luminophores and dyes for solar cells, their application in photoredox catalysis, their use as sensitizers in upconversion processes, and their performance as photochemical nitric oxide sources. The example of a luminescent Cr(0) isocyanide complex illustrates the possibility of obtaining photoactive analogues of d⁶ metal complexes that are commonly made from precious metals such as Ru(ii) or Ir(iii). The studies highlighted herein illustrate the favorable excited-state properties of robust first-row transition metal complexes with broad application potential.

Two-step model for ultrafast interfacial electron transfer: limitations of Fermi's golden rule revealed by quantum dynamics simulations

Interfacial electron transfer (IET) is one of the crucial steps in the light-harvesting process that occurs in various assemblies for solar energy conversion, such as dye-sensitized solar cells or dye-sensitized photoelectrosynthesis cells. Computational studies of IET in dye-semiconductor assemblies employ a variety of approaches, ranging from phenomenological models such as Fermi's golden rule to more complex methods relying on explicit solutions of the time-dependent Schrödinger equation. This work investigates IET in a model pyridine-TiO2 assembly, with the goals of assessing the validity of Fermi's golden rule for calculation of the IET rates, understanding the importance of conformational sampling in modeling the IET process, and establishing an approach to rapid computational screening of dye-sensitizers that undergo fast IET into the semiconductor. Our results suggest that IET is a two-step process, in which the electron is first transferred into the semiconductor surface states, followed by diffusion of the electron into the nanoparticle bulk states. Furthermore, while Fermi's golden rule and related approaches are appropriate for predicting the initial IET rate (i.e., the initial transfer of an electron from the dye into the semiconductor surface states), they are not reliable for prediction of the overall IET rate. The inclusion of conformational sampling at room temperature into the model offers a more complete picture of the IET process, leading to a distribution of IET rates with a median rate faster than the IET rate obtained for the fully-optimized structure at 0 K. Finally, the two most important criteria for determination of the initial IET rate are the percentage of electron density on the linker in the excited state as well as the number of semiconductor acceptor states available at the energy of the excited state. Both of these can be obtained from relatively simple electronic structure calculations at either ab initio or semiempirical levels of theory and can thus be used for rapid screening of dyes with the desired properties.

Nuclear inelastic scattering and density functional theory studies of a one-dimensional spin crossover [Fe(1,2,4-triazole)2(1,2,4-triazolato)](BF4) molecular chain

Nuclear inelastic scattering (NIS) experiments have been performed in order to study the vibrational dynamics of the low- and high-spin states of the polynuclear 1D spin crossover compound [Fe(1,2,4-triazole)₂(1,2,4-triazolato)](BF₄) (1). Density functional theory (DFT) calculations using the functional B3LYP* and the basis set CEP-31G for heptameric and nonameric models of the compound yielded the normal vibrations and electronic energies for high-spin and low-spin isomers of three models differing in the distribution of anionic trz^- ligands and BF₄^- anions. On the basis of the obtained energies a structural model with a centrosymmetric Fe(trzH)₄(trz^-)₂ coordination core of the mononuclear unit of the chain is proposed. The obtained distribution of the BF₄^- counteranions in the proposed structure is similar to that obtained on the basis of X-ray powder diffraction studies by Grossjean et al. (Eur. J. Inorg. Chem., 2013, 796). The NIS data of the system diluted to 10% Fe(ii) content in a 90% Zn(ii) matrix (compound (2)) show a characteristic change of the spectral pattern of the low-spin centres, compared to the low-spin phase of the parent Fe(ii) complex (1). DFT calculations reveal that this is caused by a change of the structure of the neighbours of the low-spin centres. The spectral pattern of the high-spin centres in (2) is within a good approximation identical to that of the high-spin Fe(ii) isomer of (1). The inspection of the molecular orbitals of the monomeric model systems of [Fe(trzH)₄(trz^-)₂] and [Fe(trzH)₆], together with calculations of spin transition energies, point towards the importance of an electrostatic effect caused by the negatively charged ligands. This results in the stabilisation of the low-spin state of the complex containing the anionic ligand and shortening of the Fe-N(trz^-) compared to the Fe-N(trzH) bond in high-spin, but not in low-spin [Fe(trzH)₄(trz^-)₂].

Predicting electronic structure properties of transition metal complexes with neural networks

High-throughput computational screening has emerged as a critical component of materials discovery. Direct density functional theory (DFT) simulation of inorganic materials and molecular transition metal complexes is often used to describe subtle trends in inorganic bonding and spin-state ordering, but these calculations are computationally costly and properties are sensitive to the exchange-correlation functional employed. To begin to overcome these challenges, we trained artificial neural networks (ANNs) to predict quantum-mechanically-derived properties, including spin-state ordering, sensitivity to Hartree-Fock exchange, and spin-state specific bond lengths in transition metal complexes. Our ANN is trained on a small set of inorganic-chemistry-appropriate empirical inputs that are both maximally transferable and do not require precise three-dimensional structural information for prediction. Using these descriptors, our ANN predicts spin-state splittings of single-site transition metal complexes (i.e., Cr-Ni) at arbitrary amounts of Hartree-Fock exchange to within 3 kcal mol-1 accuracy of DFT calculations. Our exchange-sensitivity ANN enables improved predictions on a diverse test set of experimentally-characterized transition metal complexes by extrapolation from semi-local DFT to hybrid DFT. The ANN also outperforms other machine learning models (i.e., support vector regression and kernel ridge regression), demonstrating particularly improved performance in transferability, as measured by prediction errors on the diverse test set. We establish the value of new uncertainty quantification tools to estimate ANN prediction uncertainty in computational chemistry, and we provide additional heuristics for identification of when a compound of interest is likely to be poorly predicted by the ANN. The ANNs developed in this work provide a strategy for screening transition metal complexes both with direct ANN prediction and with improved structure generation for validation with first principles simulation.