A Review of Density Functional Models for the Description of Fe(II) Spin-Crossover Complexes

Benchmarking Periodic Density Functional Theory Calculations for Spin-State Energies in Spin-Crossover Systems

Spin energetics is one of the biggest challenges associated with energy calculations for electronic structure methods. The energy differences of the spin states in spin-crossover compounds are very small, making them one of the most difficult systems to calculate. Few methods provide accurate results for calculating these energy differences. In addition, studies have usually focused on calculating energetics of single molecules, while spin-crossover properties are usually experimentally studied in the solid phase. In this paper, we have used periodic boundary conditions employing methods based on density functional theory to calculate the high- and low-spin energy differences for a test case of 20 extended systems. Compounds with different metals and ligands have been selected, and the results indicate that a semiquantitative description of the energy differences can be obtained with the combination of geometry optimization using the PBE functional including many-body dispersion approach and the use of meta-GGA functionals, such as r2SCAN but especially KTBM24, for the energy calculation. Other hybrid functionals, such as TPSSh, give generally good results, but the calculation of the exact exchange with periodic boundary conditions involves a huge increase in computer time and computational resources. It makes the proposed nonhybrid functional approach (KTBM24//PBE+MB) a great advantage for the study of periodic systems.

Accurate state energetics in spin-crossover systems using pure density functional theory

The energy difference between different spin states of systems with transition metals is an outstanding challenge for electronic structure calculation methods. The small energy difference between high- and low-spin states in spin-crossover systems makes most post-Hartree-Fock or density functional theory-based methods provide inaccurate values. A test case of twenty systems showing spin transitions has been used to evaluate the accuracy of a new family of training meta-GGA (Generalized Gradient Approximation) functionals. One of the functionals of this new family provides comparable or even better values than the best functional reported so far for this type of system, the TPSSh hybrid meta-GGA functional, but without having to use the exact exchange term. It also improves the results obtained with the r2SCAN meta-GGA functional, which was the best alternative to the TPSSh hybrid functional. This makes it possible to calculate the spin energetics of any kind of compound, especially large systems or periodic structures where the exact exchange requires large computational resources.

The Fe-MAN Challenge: Ferrates-Microkinetic Assessment of Numerical Quantum Chemistry

Organometallic species, such as organoferrate ions, are prototypical nucleophiles prone to reacting with a wide range of electrophiles, including proton donors. In solution, the operation of dynamic equilibria and the simultaneous presence of several organometallic species severely complicate the analysis of these fundamentally important reactions. This can be overcome by gas-phase experiments on mass-selected ions, which allow for the determination of the microscopic reactivity of the target species. In this contribution, we focus on the reactivity of a series of trisarylferrate complexes toward 2,2,2-trifluoroethanol and 2,2-difluoroethanol. By means of mass-spectrometric measurements, we determined the experimental bimolecular rate constants kexp of the gas-phase protolysis reactions of the trisarylferrate anions FePh3- and FeMes3- with the aforementioned acids. Based on these experiments, we carried out a dual blind challenge, inviting theoretical groups to submit their best predictions for the activation barriers and/or theoretical rate constants ktheo. This provides a unique opportunity to evaluate different computational protocols under minimal bias and sets the stage for further benchmarking of quantum chemical methods and data-driven approaches in the future.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.

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+.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.

Intramolecular Hydrogen Bond in Pyridine Schiff Bases as Ancillary Ligands of Re(I) Complexes Is a Switcher between Visible and NIR Emissions: A Relativistic Quantum Chemistry Study

Rhenium(I) tricarbonyl complexes have been described as suitable fluorophores, particularly for biological applications. fac-[Re(CO)₃(N,N)L]^(0 or 1+) complexes, where N,N is a substituted dinitrogenated ligand (bipyridine or derivatives with relatively small substituents) and L the ancillary ligand [a pyridine Schiff base (PSB) harboring an intramolecular hydrogen bond (IHB)], have presented promissory results concerning their use as fluorophores, especially for walled cells (i.e., bacteria and fungi). In this work, we present a relativistic theoretical analysis of two series of fac-[Re(CO)₃(N,N)PSB]¹⁺ complexes to predict the role of the IHB in the ancillary ligand concerning their photophysical behavior. N,N corresponds to 2,2'-bipyridine (bpy) (series A) or 4,4'-bis(ethoxycarbonyl)-2,2'-bipyridine (deeb) (series B). We found that all the complexes present absorption in the visible light range. In addition, complexes presenting a PSB with an IHB exhibit luminescent emission suitable for biological purposes: large Stokes shift, emission in the range of 600-700 nm, and τ in the order of 10^-2 to 10^-3 s. By contrast, complexes with PSB lacking the IHB show a predicted emission with the lowest triplet excited-state energy entering the NIR region. These results suggest a role of the IHB as an important switcher between visible and NIR emissions in this kind of complexes. Since the PSB can be substituted to modulate the properties of the whole Re(I) complex, it will be interesting to explore whether other substitutions can also affect the photophysical properties, mainly the emission range.

Evolution of Vibrational Spectra in the Manganese-Silicon Clusters Mn2Sin, n = 10, 12, and 13, and Cationic [Mn2Si13]. J Phys Chem A 2022;126:1617-1626. [PMID: 35238570 PMCID: PMC9084549 DOI: 10.1021/acs.jpca.1c10027]

A comparison of DFT-computed and measured infrared spectra reveals the ground state structures of a series of gas-phase silicon clusters containing a common Mn₂ unit. Mn₂Si₁₂ and [Mn₂Si₁₃]⁺ are both axially symmetric, allowing for a clean separation of the vibrational modes into parallel (a₁) and perpendicular (e₁) components. Information about the Mn–Mn and Mn–Si bonding can be extracted by tracing the evolution of these modes as the cluster increases in size. In [Mn₂Si₁₃]⁺, where the antiprismatic core is capped on both hexagonal faces, a relatively simple spectrum emerges that reflects a pseudo-D_6d geometry. In cases where the cluster is more polar, either because there is no capping atom in the lower face (Mn₂Si₁₂) or the capping atom is present but displaced off the principal axis (Mn₂Si₁₃), the spectra include additional features derived from vibrational modes that are forbidden in the parent antiprism.

Accurate calculation of spin-state energy gaps in Fe(III) spin-crossover systems using density functional methods

Fe(III) complexes are receiving ever-increasing attention as spin crossover (SCO) systems because they are usually air stable, as opposed to Fe(II) complexes, which are prone to oxidation. Here, we present the first systematic study exclusively devoted to assess the accuracy of several exchange-correlation functionals when it comes to predicting the energy gap between the high-spin (S = 5/2) and the low-spin (S = 1/2) states of Fe(III) complexes. Using a dataset of 24 different Fe(III) hexacoordinated complexes, it is demonstrated that the B3LYP* functional is an excellent choice not only for predicting spin-state energy gaps for Fe(III) complexes undergoing spin-transitions but also for discriminating Fe(III) complexes that are either low- or high-spin in the whole range of temperatures. Our benchmark study has led to the identification of a very versatile Fe(III) compound whose SCO properties can be engineered upon changing a single axial ligand. Overall, this work demonstrates that B3LYP* is a reliable functional for screening new spin-crossover systems with tailored properties.