Dealing with Spin States in Computational Organometallic Catalysis

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin-state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six FeIII or FeII complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin-state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way-in the form of single or double inequalities-are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin-state splittings of [FeIII(P)(2-MeIm)2]+, [FeIII(P)(2-MeIm)]+, [FeII(P)(THF)2] and [FeII(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in FeIII porphyrins. The present approach, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for metalloporphyrins, which are important models to understand the electronic properties of heme proteins.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Metastable Charged Dimers in Organometallic Species: A Look into Hydrogen Bonding between Metallocene Derivatives

Multiply charged complexes bound by noncovalent interactions have been previously described in the literature, although they were mostly focused on organic and main group inorganic systems. In this work, we show that similar complexes can also be found for organometallic systems containing transition metals and deepen in the reasons behind the existence of these species. We have studied the structures, binding energies, and dissociation profiles in the gas phase of a series of charged hydrogen-bonded dimers of metallocene (Ru, Co, Rh, and Mn) derivatives isoelectronic with the ferrocene dimer. Our results indicate that the carboxylic acid-containing dimers are more strongly bonded and present larger barriers to dissociation than the amide ones and that the cationic complexes tend to be more stable than the anionic ones. Additionally, we describe for the first time the symmetric proton transfer that can occur while in the metastable phase. Finally, we use a density-based energy decomposition analysis to shine light on the nature of the interaction between the dimers.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Toward a Reliable Theory Benchmark

A new composite method for the calculation of spin-crossover energies in 3d transition-metal complexes based on multireference methods is presented. The method reduces to MRCISD+Q at the complete-basis-set (CBS) level for atomic ions, for which it gives excitation energies with a mean absolute error of only ca. 0.01 eV. For molecular complexes, the CASPT2+δMRCI composite approach corresponds to a CASPT2/CBS calculation augmented by a high-level MRCISD+Q-CASPT2 correction with a smaller ligand basis set. For a set of [Fe(He)6]n+ test complexes, the approach reproduces full MRCISD+Q/CBS results to within better than 0.04 eV, without depending on any arbitrary IPEA shifts. The high-quality CASPT2+δMRCI method has then been applied to a series of 3d transition-metal hexaqua complexes in aqueous solution, augmented by an elaborate 3D-RISM-SCF solvent treatment of the underlying structures. It provides unprecedented agreement with experiment for the lowest-lying vertical spin-flip excitation energies, except for the Fe³⁺ system. Closer examination of the latter case provides strong evidence that the observed lowest-energy excitation at 1.56 eV, which has been used frequently for evaluating quantum-chemical methods, does not arise from the iron(III) hexaqua complex in solution, but from its singly deprotonated counterpart, [Fe(H2O)5OH]2+.

Direct Benzene Hydroxylation with Dioxygen Induced by Copper Complexes: Uncovering the Active Species by DFT Calculations

The direct oxidation of benzene into phenol using molecular oxygen at very mild temperatures can be promoted in the presence of the copper complex Tp^Br3Cu(NCMe) in the homogeneous phase in the presence of ascorbic acid as the source of protons and electrons. The stoichiometric nature, relative to copper, of this transformation prompted a thorough DFT study in order to understand the reaction pathway. As a result, the dinuclear species Tp^Br3Cu^II(μ-O^•)(μ-OH)Cu^IITp^Br3 is proposed as the relevant structure which is responsible for activating the arene C–H bond leading to phenol formation.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T₁) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Experimental and Computational Insight into the Mechanism of NO Binding to Ferric Microperoxidase. The Likely Role of Tautomerization to Account for the pH Dependence

According to the current paradigm, the metal-hydroxo bond in a six-coordinate porphyrin complex is believed to be significantly less reactive in ligand substitution than the analogous metal-aqua bond, due to a much higher strength of the former bond. Here, we report kinetic studies for nitric oxide (NO) binding to a heme-protein model, acetylated microperoxidase-11 (AcMP-11), that challenge this paradigm. In the studied pH range 7.4-12.6, ferric AcMP-11 exists in three acid-base forms, assigned in the literature as [(AcMP-11)FeIII(H2O)(HisH)] (1), [(AcMP-11)FeIII(OH)(HisH)] (2), and [(AcMP-11)FeIII(OH)(His-)] (3). From the pH dependence of the second-order rate constant for NO binding (kon), we determined individual rate constants characterizing forms 1-3, revealing only a ca. 10-fold decrease in the NO binding rate on going from 1 (kon(1) = 3.8 × 106 M-1 s-1) to 2 (kon(2) = 4.0 × 105 M-1 s-1) and the inertness of 3. These findings lead to the abandonment of the dissociatively activated mechanism, in which the reaction rate can be directly correlated with the Fe-OH bond energy, as the mechanistic explanation for the process with regard to 2. The reactivity of 2 is accounted for through the existence of a tautomeric equilibrium between the major [(AcMP-11)FeIII(OH)(HisH)] (2a) and minor [(AcMP-11)FeIII(H2O)(His-)] (2b) species, of which the second one is assigned as the NO binding target due to its labile Fe-OH2 bond. The proposed mechanism is further substantiated by quantum-chemical calculations, which confirmed both the significant labilization of the Fe-OH2 bond in the [(AcMP-11)FeIII(H2O)(His-)] tautomer and the feasibility of the tautomer formation, especially after introducing empirical corrections to the computed relative acidities of the H2O and HisH ligands based on the experimental pKa values. It is shown that the "effective lability" of the axial ligand (OH-/H2O) in 2 may be comparable to the lability of the H2O ligand in 1.

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.