Assessment of Density Functionals for the High-Spin/Low-Spin Energy Difference in the Low-Spin Iron(II) Tris(2,2′-bipyridine) Complex

Improving the Accuracy in the Prediction of Transition-Metal Spin-State Energetics Using a Robust Variation-Based Approach: Density Functional Theory, CASPT2 and MC-PDFT Applied to the Case Study of Tris-Diimine Fe(II) Complexes

Designing ligands for transition metal complexes with a specified low-spin, high-spin or spin-crossover behavior is challenging. A major advance was recently made by Phan et al. [J. Am. Chem. Soc. 2017, 139, 6437-6447] who showed that the spin state of a homoleptic tris-diimine Fe(II) complex can be predicted from the N-N distance in the free diimine. They could thus predict the change in magnetic behavior on passing from the complexes of 2,2'-bipyridine (bpy), 2,2'-biimidazole (bim) and 2,2'-bis-2-imidazoline (bimz) ligands to those obtained with the modified analogs 4,5-diazafluoren-9-one (dafo), 1,1'-(α,α'-o-xylyl)-2,2'-bisimidazole (xbim) and 2,3,5,6,8,9-hexahydrodiimidazo[1,2-a:2', 1'-c]pyrazine (etbimz), respectively. Theoretically, the challenge lies in the accurate determination of the HS-LS zero-point energy difference ΔEHL°. The issue can be circumvented by using a variation-based approach, wherein ΔEHL° is not directly evaluated but obtained from the estimate of its variation Δ(ΔEHL°) in series of related systems, which include one whose ΔEHL° is accurately known [Phys. Chem. Chem. Phys. 2013, 15, 3752-3763; J. Phys. Chem. A 2022, 126, 6221-6235]. In this study, density functional theory (DFT), second-order multireference perturbation theory in its CASPT2 formulation, multiconfigurational pair DFT (MC-PDFT) and its hybrid formulation (HMC-PDFT) have been applied to the determination of Δ(ΔEHL°) in the pairs of complexes ( [ F e ( b p y ) 3 ] 2 + , [ F e ( d a f o ) 3 ] 2 + ) , ( [ F e ( b i m ) 3 ] 2 + , [ F e ( x b i m ) 3 ] 2 + ) and ( [ F e ( b i m z ) 3 ] 2 + , [ F e ( e t b i m z ) 3 ] 2 + ) . In DFT, we used several semilocal functionals and their global hybrids, as well as their D2, D3, D3BJ and D4 dispersion-corrected forms; and in MC-PDFT, different translated and fully translated functionals. The results are consistent with one another and in very good agreement with experiments. They show small to vanishing dependence on key details of the methods used: namely, the exact-exchange contribution to global hybrids; the ionization potential-electron affinity shift and basis sets used in the CASPT2 calculations; and the active spaces employed for the CASSCF wave functions used in the MC-PDFT and HMC-PDFT calculations. Insights into the change in the spin-state energetics accompanying the ligand exchanges were gained through a complexation energy analysis. Using the accurate CCSD(T) estimate of the HS-LS adiabatic energy difference in [ F e ( N C H ) 6 ] 2 + [J. Chem. Theory Comput. 2012, 8, 4216-4231], the Δ(ΔEHL°)-approach has been applied to the determination of ΔEHL° in the diimine complexes. The CASPT2 and DFT-D2 methods only give results in agreement with experiments. This suggests for the other methods a limitation in their treatment of dispersion which prevents them from accurately describing the spin-state energetics change accompanying the passing from [ F e ( N C H ) 6 ] 2 + with the tetragonal arrangement of its nitrile ligands to the tris-diimine complexes with the trigonal packing of their bulkier ligands.

Tuning the spin-crossover properties of [Fe2] metal-organic cages

A computational study on the interplay between ligand functionalization and guest effects on the transition temperature (T1/2) in the [Fe2(L1R)3]@X (L1 = 1,3-bis-(3-(pyridin-2-yl)-1H-pyrazol-5-yl)benzene, X = H-, F-, Cl-, Br-, I- and [BF4]-, R = H, F, or CH3) family of metal-organic cages (MOCs) is presented. Our results indicate that ligand functionalization with electron-donating or electron-withdrawing groups can significantly impact the T1/2 as expected, while the guest effect in lowering the T1/2 has a linear correlation with the increasing guest size. More importantly, small guests can move away from the center of the cavity, thus enhancing the two-step characteristic of the transition. All the data can be understood by analyzing the underlying electronic structure of the studied systems in terms of the relevant d-based molecular orbitals. These results can help in the rational design of new MOCs that can operate as sensors at specific temperatures, thus accelerating the discovery of new SCO devices with tailored properties.

Antifungal activity of Co(II) and Cu(II) complexes containing 1,3-bis(benzotriazol-1-yl)-propan-2-ol on the growth and virulence traits of fluconazole-resistant Candida species: synthesis, DFT calculations, and biological activity

Relevant virulence traits in Candida spp. are associated with dimorphic change and biofilm formation, which became an important target to reduce antifungal resistance. In this work, Co(II) complexes containing a benzotriazole derivative ligand showed a promising capacity of reducing these virulence traits. These complexes exhibited higher antifungal activities than the free ligands against all the Candida albicans and non-albicans strains tested, where compounds 2 and 4 showed minimum inhibitory concentration values between 15.62 and 125 μg mL-1. Moreover, four complexes (2-5) of Co(II) and Cu(II) with benzotriazole ligand were synthesized. These compounds were obtained as air-stable solids and characterized by melting point, thermogravimetric analysis, infrared, Raman and ultraviolet/visible spectroscopy. The analysis of the characterization data allowed us to identify that all the complexes had 1:1 (M:L) stoichiometries. Additionally, Density Functional Theory calculations were carried out for 2 and 3 to propose a probable geometry of both compounds. The conformer Da of 2 was the most stable conformer according to the Energy Decomposition Analysis; while the conformers of 3 have a fluxional behavior in this analysis that did not allow us to determine the most probable conformer. These results provide an important platform for the design of new compounds with antifungal activities and the capacity to attack other target of relevance to reduce antimicrobial resistance.

Ultrafast Spin Crossover Photochemical Mechanism in [FeII(2,2'-bipyridine)3]2+] Revealed by Quantum Dynamics

Photoexcitation of [FeII(2,2'-bipyridine)3]2+ induces a subpicosecond spin crossover transformation from a low-spin singlet to a high-spin quintet state. The mechanism involves metal-centered (MC) and metal-ligand charge transfer (MLCT) triplet intermediates, but their individual contributions to this efficient intersystem crossing have been object of debate. Employing quantum wavepacket dynamics, we show that MC triplets are catalyzing the transfer to the high-spin state. This photochemical pathway is made possible thanks to bipyridine stretching vibrations, facilitating the conversion between the MLCT bands to such MC triplets. We show that the lifetime of the MLCT states can be increased to tens of picoseconds by breaking the conjugation between pyridine units, which increases the energetic gap between MLCT and MC states. This opens the route for the design of new chelating ligands inducing long-lived MLCT states in iron complexes.

A new freely-downloadable hands-on density-functional theory workbook using a freely-downloadable version of deMon2k

A hands-on workbook for density-functional theory (DFT) has been developed that can be used to provide practical teaching for students at the Masters or advanced undergraduate level that is free, can be used on a student’s own personal computer, and complements formal course work. The workbook is also very much intended to encourage students to explore program options, discover theory limitations, puzzle out what to do when the program does not work as expected, and to help students transition to thinking and using quantum chemistry programs as a researcher might do. After describing the structure of the workbook, we describe how the workbook has been used thus far as a teaching tool and as a useful step towards research-level problems.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the U_eff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of U_eff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble U_eff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional U_eff values. Based on the observation that the U_eff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged U_eff values for high-throughput calculations.

Environmental Control of the Magnetic Behavior of Transition Metal Complexes: Density Functional Theory Study of Zeolite Y Embedded Complexes [M(bpy)3]2+@Y (M = Fe2+, Co2+)

Using the supramolecular approach developed for the study of the guest-host interactions in the zeolite Y encapsulated [Fe(bpy)₃]²⁺ compound: [Fe(bpy)₃]²⁺@Y (bpy = 2,2'-bipyridine) [Vargas et al., J. Chem. Theory Comput. 2009, 5, 97-115], we apply density functional theory (DFT) to the study of the influence of zeolite Y encapsulation on the structural and energetic properties of [Co(bpy)₃]²⁺ in the low-spin (LS) and high-spin (HS) states, while revisiting [Fe(bpy)₃]²⁺@Y. Although the accurate prediction of the HS-LS energy difference ΔE_HL^el remains challenging for current DFT methods, they give accurate estimates of its variation Δ(ΔE_HL^el) in a series of complexes of a given transition metal ion. Therefore, denoting [M(bpy)₃]²⁺@Y_SM as the supramolecular model of the inclusion compounds, the values of ΔE_HL^el for the bpy complexes in the gas phase and in the supercage of zeolite Y were determined by combining the DFT estimates of Δ(ΔE_HL^el) in the series {[M(NCH)₆]²⁺, [M(bpy)₃]²⁺, and [M(bpy)₃]²⁺@Y_SM}, with accurate CCSD(T) estimates of ΔE_HL^el in the benchmark complexes [M(NCH)₆]²⁺ (M = Fe, Co) [Lawson Daku et al., J. Chem. Theory Comput., 2012, 8, 4216-4231]. Generalized gradient approximations as well as global and range-separated hybrids were employed. In order to better account for the key role of dispersion, they were also augmented with the semiempirical D2, D3BJ, and D3BJM dispersion corrections when available. The use of the D3BJ and D3BJM corrections led to similar results, and this is only with the use of the D2 scheme that (i) the free and encapsulated [Fe(bpy)₃]²⁺ are correctly predicted as LS species and that (ii) the encapsulation of both complexes translates into a destabilization of their HS state with respect to their LS state. The increase of the HS-LS energy difference is smaller for [Co(bpy)₃]²⁺ than [Fe(bpy)₃]²⁺ because the HS-LS molecular volume difference ΔV_HL in [Co(bpy)₃]²⁺ is ∼50% smaller than in [Fe(bpy)₃]²⁺. Periodic DFT calculations performed on crystalline [M(bpy)₃]²⁺@Y show that the employed [M(bpy)₃]²⁺@Y_SM supramolecular model allows the influence of encapsulation on the geometry and the spin-state energetics of [M(bpy)₃]²⁺ (M = Fe, Co) to be quantitatively captured.

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.

Trend in light-induced excited-state spin trapping in Fe(II)-based spin crossover systems

A computational study of the light-induced excited spin-state trapping (LIESST) in a number of Fe(II) spin crossover complexes, coordinated by monodentate, bidentate and multidentate ligands is carried out, with the goal to uncover the trend in the low temperature relaxation rate. A nine order of magnitude change in low temperature relaxation rate is observed among the complexes. The trend is rationalized in terms of the change in metal-ligand covalency, numerically estimated by the crystal orbital Hamiltonian population, thus influencing the back donation or delocalization of the electrons from the low-lying Fe(II)-centered molecular orbital to the empty low-lying ligand-centered π* antibonding molecular orbitals.

Benchmarking Plane Waves Quantum Mechanical Calculations of Iron(II) Tris(2,2′-bipyridine) Complex by X-ray Absorption Spectroscopy

In this work, we used, for the first time, a computational Self-Consistent Field procedure based on plane waves to describe the low and high spin conformational states of the complex [Fe(bpy)3]2+. The results obtained in the study of the minimum energy structures of this complex, a prototype of a wide class of compounds called Spin Cross Over, show how the plane wave calculations are in line with the most recent studies based on gaussian basis set functions and, above all, reproduce within acceptable errors the experimental spectra of X-ray absorption near-edge structure spectroscopy (XANES). This preliminary study shows the capabilities of plane wave methods to correctly describe the molecular structures of metal-organic complexes of this type and paves the way for future even complex computational simulations based on the energy gradient, such as Nudge Elastic Band or ab-initio Born-Oppenheimer molecular dynamics.

CASPT2 molecular geometries of Fe(II) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. We recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe-ligand bond distances.

Hidden ordered structure in the archetypical Fe(pyrazine)[Pt(CN)4] spin-crossover porous coordination compound

The actual low-spin state of Fe(pyrazine)Pt(CN)4 implies an ordered arrangement of the pyrazine rings, which significantly affects the spin transition.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

A Theoretical Assessment of Spin and Charge States in Binuclear Cobalt-Ruthenium Complexes: Implications for a Creutz-Taube Model Ion Separated by a C60-Derivative Bridging Ligand

We investigate the spin-state energetics and the role of ionic charges in the electronic configuration of binuclear complexes of the form [(NH₃)₅Co(py)-X-(py)Ru(NH₃)₅]^q+. In these compounds with q = 4-6, py = pyridine, and X = C≡C and C₆₀, the Co-Ru distance varies from ∼1.4 to ∼2.1 nm. We carry out a systematic electronic structure calculation using different exchange-correlation (xc) approaches within spin-density functional theory, which are largely employed to investigate the properties of a variety of coordination complexes. To evaluate the effects of spin states and type of spacer in the bridging ligand on the valence tautomerism between Co^2+/3+ and Ru^2+/3+, we examine in more detail the case of Creutz-Taube-type ions [(NH₃)₅Co(py)-X-(py)Ru(NH₃)₅]⁵⁺. Our analysis shows that the stabilization of low- and high-spin states critically depends on the total charge of the complex, type of X-bridged ligand, and employed xc approach to calculate the electron spin density. Importantly, the C₆₀-bridged group may result in a blockage of the valence tautomerism of the Creutz-Taube complex, inducing bistable charge configurations. Overall, our results also show that an adiabatic description in terms of the frontier molecular spin-orbitals for analyzing the distinct spin-charge states of these complexes may dramatically depend on the density-functional description.

Quantum-chemistry-aided ligand engineering for potential molecular switches: changing barriers to tune excited state lifetimes

Substitution of terpyridine at the 4' position with electron withdrawing and donating groups is used to tune the quintet lifetime of its iron(ii) complex. DFT calculations suggest that the energy barrier between the quintet and singlet states can be altered significantly upon substitution, inducing a large variation of the lifetime of the photoexcited quintet state. This prediction was experimentally verified by transient optical absorption spectroscopy and good agreement with the trend expected from the calculations was found. This demonstrates that the potential energy landscape can indeed be rationally tailored by relevant modifications based on DFT predictions. This result should pave the way to advancing efficient theory-based ligand engineering of functional molecules to a wide range of applications.

Exploring the light-induced dynamics in solvated metallogrid complexes with femtosecond pulses across the electromagnetic spectrum

Oligonuclear complexes of d⁴-d⁷ transition metal ion centers that undergo spin-switching have long been developed for their practical role in molecular electronics. Recently, they also have appeared as promising photochemical reactants demonstrating improved stability. However, the lack of knowledge about their photophysical properties in the solution phase compared to mononuclear complexes is currently hampering their inclusion into advanced light-driven reactions. In the present study, the ultrafast photoinduced dynamics in a solvated [2 × 2] iron(II) metallogrid complex are characterized by combining measurements with transient optical-infrared absorption and x-ray emission spectroscopy on the femtosecond time scale. The analysis is supported by density functional theory calculations. The photocycle can be described in terms of intra-site transitions, where the Fe^II centers in the low-spin state are independently photoexcited. The Franck-Condon state decays via the formation of a vibrationally hot high-spin (HS) state that displays coherent behavior within a few picoseconds and thermalizes within tens of picoseconds to yield a metastable HS state living for several hundreds of nanoseconds. Systematic comparison with the closely related mononuclear complex [Fe(terpy)₂]²⁺ reveals that nuclearity has a profound impact on the photoinduced dynamics. More generally, this work provides guidelines for expanding the integration of oligonuclear complexes into new photoconversion schemes that may be triggered by ultrafast spin-switching.

Influence of Varying Functionalization on the Peroxidase Activity of Nickel(II)–Pyridine Macrocycle Catalysts: Mechanistic Insights from Density Functional Theory

Nickel(II) complexes of mono-functionalized pyridine-tetraazamacrocycles (PyMACs) are a new class of catalysts that possess promising activity similar to biological peroxidases. Experimental studies with ABTS (2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid), substrate) and H2O2 (oxidant) proposed that hydrogen-bonding and proton-transfer reactions facilitated by their pendant arm were responsible for their catalytic activity. In this work, density functional theory calculations were performed to unravel the influence of pendant arm functionalization on the catalytic performance of Ni(II)–PyMACs. Generated frontier orbitals suggested that Ni(II)–PyMACs activate H2O2 by satisfying two requirements: (1) the deprotonation of H2O2 to form the highly nucleophilic HOO−, and (2) the generation of low-spin, singlet state Ni(II)–PyMACs to allow the binding of HOO−. COSMO solvation-based energies revealed that the O–O Ni(II)–hydroperoxo bond, regardless of pendant arm type, ruptures favorably via heterolysis to produce high-spin (S = 1) [(L)Ni3+–O·]2+ and HO−. Aqueous solvation was found crucial in the stabilization of charged species, thereby favoring the heterolytic process over homolytic. The redox reaction of [(L)Ni3+–O·]2+ with ABTS obeyed a 1:2 stoichiometric ratio, followed by proton transfer to produce the final intermediate. The regeneration of Ni(II)–PyMACs at the final step involved the liberation of HO−, which was highly favorable when protons were readily available or when the pKa of the pendant arm was low.

DFT Study of the CNS Ligand Effect on the Geometry, Spin-State, and Absorption Spectrum in Ruthenium, Iron, and Cobalt Quaterpyridine Complexes

Geometry parameters, total energy of the system in different spin states, harmonic vibrational frequencies, and absorption spectra were computed for a range of mononuclear quaterpyridine Ru(II), Fe(III/II), and Co(III/II) complexes with two axial ambidentate CNS ligands by using density functional theory (DFT) and time-dependent DFT calculations. Both structural and electronic properties were found to be correlating with the type of the binding atom in the CNS ligand (isomerization differs by 4-13 kcal·mol-1). The N-bonding of CNS ligands is energetically favored. It was also found that the low spin (LS) state is the ground state for both Ru(II) and Co(III) complexes regardless of the CNS arrangement. The other complexes are the high-spin (HS) ground-state ones with the only exception of the S-bonded CNS isomer of the Fe(III) complex. The dependencies of energy differences between the HS and LS states versus C demonstrated stabilization of the HS state with an increasing amount of the exact exchange admixture (C) for iron and cobalt complexes. An opposite behavior was observed for ruthenium complexes. The best match in harmonic vibrational frequencies between the experimental and calculated values has been reached at C = 0.15 for all the complexes. The absorption profile of the Fe(II) complex with the alternatively bonded CNS ligands strongly depends on the angle between them. The light-harvesting efficiency of the Fe(II) complexes is very similar (∼0.4) and sufficiently close to that of the Ru(II) complexes. The iron-based coordination compounds are considered as a prospective dye for dye-sensitized solar cells. The results of calculations were completed with experimental reference data, thus providing a systematic compendium for practical use.

Benchmarking quantum chemistry methods for spin-state energetics of iron complexes against quantitative experimental data

The accuracy of relative spin-state energetics predicted by selected quantum chemistry methods: coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation theory (CASPT2, NEVPT2), multireference configuration interaction at the MRCISD+Q level, and a number of DFT methods, is quantitatively evaluated by comparison with the experimental data of four octahedral iron complexes. The available experimental data, either spin-forbidden transition energies or spin crossover enthalpies, are corrected for relevant environmental effects in order to derive the quantitative benchmark set of iron spin-state energetics. Comparison of theory predictions with the resulting reference data: (1) validates the high accuracy of the CCSD(T) method, particularly when based on Kohn-Sham orbitals, giving the maximum error below 2 kcal mol-1 and the mean absolute error (MAE) below 1 kcal mol-1; (2) corroborates the tendency of CASPT2 to systematically overstabilize higher-spin states by up to 5.5 kcal mol-1; (3) confirms that the latter problem is partly remedied by the recently proposed CASPT2/CC approach [Phung et al., J. Chem. Theory Comput., 2018, 14, 2446-2455]; (4) demonstrates that NEVPT2 performs worse than CASPT2, by giving errors up to 7 kcal mol-1; (5) shows that the accuracy of MRCISD+Q spin-state energetics strongly depends on the size-consistency correction: the Davidson-Silver and Pople corrections perform best (MAE < 3 kcal mol-1), whereas the standard Davidson correction is not recommended (MAE of 7 kcal mol-1). Only a few DFT methods (including the best performing ones identified in this study: B2PLYP-D3 and OPBE) are able to provide a balanced description of the spin-state energetics for all four studied iron complexes simultaneously, corroborating the non-universality problem of approximate density functionals.

Excited-state solvation structure of transition metal complexes from molecular dynamics simulations and assessment of partial atomic charge methods

Excited-state solvation structure (radial distribution function) of transition metal complexes by classical and mixed quantum-classical (QM/MM) molecular dynamics simulations.

Synthetic Fe/Cu Complexes: Toward Understanding Heme-Copper Oxidase Structure and Function

Heme-copper oxidases (HCOs) are terminal enzymes on the mitochondrial or bacterial respiratory electron transport chain, which utilize a unique heterobinuclear active site to catalyze the 4H+/4e- reduction of dioxygen to water. This process involves a proton-coupled electron transfer (PCET) from a tyrosine (phenolic) residue and additional redox events coupled to transmembrane proton pumping and ATP synthesis. Given that HCOs are large, complex, membrane-bound enzymes, bioinspired synthetic model chemistry is a promising approach to better understand heme-Cu-mediated dioxygen reduction, including the details of proton and electron movements. This review encompasses important aspects of heme-O2 and copper-O2 (bio)chemistries as they relate to the design and interpretation of small molecule model systems and provides perspectives from fundamental coordination chemistry, which can be applied to the understanding of HCO activity. We focus on recent advancements from studies of heme-Cu models, evaluating experimental and computational results, which highlight important fundamental structure-function relationships. Finally, we provide an outlook for future potential contributions from synthetic inorganic chemistry and discuss their implications with relevance to biological O2-reduction.

UNO DMRG CAS CI calculations of binuclear manganese complex Mn(IV)2 O2 (NHCHCO2 )4 : Scope and applicability of Heisenberg model

Both direct exchange and super-exchange interactions cooperate to realize inter-spin magnetic interaction in binuclear manganese complex Mn(IV)₂ O₂ (NHCHCO₂ )₄ with a di-μ-oxo path. We revisited this spin system using DMRG CAS methods and CAS selection procedures. Our results indicate that our previous "dynamically extended spin polarization" (DE-SP) procedure for organic polyradicals and so forth does not work well. Thus, we have examined another selection procedure, the "dynamically extended super-exchange" (DE-SE) procedure. DMRG CASCI [18,18] by UB3LYP(HS)-UNO(DE-SE) can realize antiferromagnetic J values similar to experimental ones (-87 cm^-1 ). In addition, all J values between all spin states (HS[septet],IS[quintet],IS[triplet],LS[singlet])were also shown to be correct under sufficiently large M values. © 2018 Wiley Periodicals, Inc.

Monitoring Ultrafast Spin Crossover Intermediates in an Iron(II) Complex by Broad Band Stimulated X-ray Raman Spectroscopy

The photoinduced spin crossover dynamics of transition metal complexes is of fundamental scientific importance and is used for sensor device applications and solar energy harvesting. Current X-ray and optical spectroscopy experiments for [Fe^II(bpy)₃], an archetypal earth-abundant metal complex, show conflicting spin dynamics. We have simulated the broad band transient X-ray absorption and hybrid (broad + narrow band) X-ray stimulated Raman signals at the N and Fe K-edges of the key excited state intermediates involved in the spin crossover process of this complex. We find that these signals are much more sensitive to electron and spin populations than transition absorption and may be useful in the design of photovoltaic and artificial photosynthetic systems.

Molecular Modeling Study toward Development of H2S-Free Removal of Iron Sulfide Scale from Oil and Gas Wells

A common problem that faces the oil and gas industry is the formation of iron sulfide scale in various stages of production. Recently an effective chemical formulation was proposed to remove all types of iron sulfide scales (including pyrite), consisting of a chelating agent diethylenetriaminepentaacetic acid (DTPA) at high pH using potassium carbonate (K₂CO₃). The aim of this molecular modeling study is to develop insight into the thermodynamics and kinetics of the chemical reactions during scale removal. A cluster approach was chosen to mimic the overall system. Standard density functional theory (B3LYP/6-31G*) was used for all calculations. Low spin K₄Fe(II)₄(S₂H)₁₂ and K₃Fe(II)(S₂H)₅ clusters were derived from the crystal structure of pyrite and used as mimics for surface scale FeS₂. In addition, K₅DTPA was used as a starting material too. High spin K₃Fe(II)DTPA, and K₂S₂ were considered as products. A series of K _m Fe(II)(S₂H) _n complexes (m = n-2, n = 5-0) with various carboxylate and glycinate ligands was used to establish the most plausible reaction pathway. Some ligand exchange reactions were investigated on even simpler Fe(II) complexes in various spin states. It was found that the dissolution of iron sulfide scale with DTPA under basic conditions is thermodynamically favored and not limited by ligand exchange kinetics as the activation barriers for these reactions are very low. Singlet-quintet spin crossover and aqueous solvation of the products almost equally contribute to the overall reaction energy. Furthermore, seven-coordination to Fe(II) was observed in both high spin K₃Fe(II)DTPA and K₂Fe(II)(EDTA)(H₂O) albeit in a slightly different manner.

Spin-Crossover Temperature Predictable from DFT Calculation for Iron(II) Complexes with 4-Substituted Pybox and Related Heteroaromatic Ligands

Spin-crossover (SCO) is a reversible transition between low and high spin states by external stimuli such as heat. The SCO behavior and transition temperature (T _1/2) of a series of [Fe^II(X-pybox)₂](ClO₄)₂ were studied to establish a methodology for ligand-field engineering, where X-pybox stands for 2,6-bis(oxazolin-2-yl)pyridine substituted with X at the 4-position of the pyridine ring. We utilized X = MeO, Me, 3-thienyl, Ph, H, MeS, 2-thienyl, N₃, Cl, Br, 3-pyridyl, and 4-pyridyl. The solution susceptometry on five new derivatives with X = Me, 2-thienyl, N₃, Br, and 3-pyridyl was performed in acetone, giving the SCO temperatures of 220, 260, 215, 280, and 270 K, respectively. The density-functional-theory molecular orbital (MO) calculation was performed on the ligands with geometry optimization. The atomic charge on the pyridine nitrogen atom [ρ(N_py)] was extracted from the natural orbital population analysis. Positive correlation appeared in the T _1/2 versus ρ(N_py) plot with R ² = 0.734, being consistent with the analysis using the Hammett substituent constants (σ_p and σ_p ⁺). This finding well agrees with the mechanism proposed: the rich electron density lifts the t_2g energy level through the dπ-pπ interaction, resulting in a narrow t_2g-e_g energy gap and favoring the high-spin state and low T _1/2. The MO method was successfully applied to the known SCO-active iron(II) compounds involving 4-substituted 2,6-bis(pyrazol-1-yl)pyridines. A distinct positive correlation appeared in the T _1/2 versus ρ(N_py) plot. The comparison of correlation coefficients indicates that ρ(N_py) is a more reliable parameter than σ_p or σ_p ⁺ to predict a shift of T _1/2. Furthermore, this method can be more generalized by application to another known SCO family having 3-azinyl-4-p-tolyl-5-phenyl-1,2,4-triazole ligand series, where azinyl stands for a 2-azaaromatic ring. A good linear correlation was found in the T _1/2 versus ρ(N_A) plot (N_A is the ligating nitrogen atom in the azaaromatic ring). Finally, we will state a reason why the present treatment is competent to predict the SCO equilibrium position only by consideration on the electronic perturbation.

Redox Potentials and Electronic States of Iron Porphyrin IX Adsorbed on Single Crystal Gold Electrode Surfaces

Metalloporphyrins are active sites in metalloproteins and synthetic catalysts. They have also been studied extensively by electrochemistry as well as being prominent targets in electrochemical scanning tunneling microscopy (STM). Previous studies of FePPIX adsorbed on graphite and alkylthiol modified Au electrodes showed a pair of reversible Fe(III/II)PPIX peaks at about -0.41 V (vs NHE) at high solution pH. We recently used iron protoporphyrin IX (FePPIX) as an intercalating probe for long-range electrochemical electron transfer through a G-quadruplex oligonucleotide (DNAzyme); this study disclosed two, rather than a single pair of voltammetric peaks with a new and dominating peak, shifted 200 mV positive relative to the ≈-0.4 V peak. Prompted by this unexpected observation, we report here a study of the voltammetry of FePPIX itself on single-crystal Au(111), (100), and (110) and polycrystalline Au electrode surfaces. In all cases the dominating pair of new Fe(III/II)PPIX redox peaks, shifted positively by more than 200 mV compared to those of previous studies appeared. This observation is supported by density functional theory (DFT) which shows that strong dispersion forces in the FePPIX/Au electronic interaction drive the midpoint potential toward positive values. The FePPIX spin states depend on interaction with the Au(111) interface, converting all the Fe(II)/(III)PPIX species into low-spin states. These results support electrochemical evidence for the nature of the electronic coupling between FePPIX and Au-surfaces, and the electronic states of adsorbate molecules, with a bearing also on recent reports of magnetic FePPIX/Au(111) interactions in ultrahigh vacuum (UHV).

Reactivity of Tantalum Carbide Cluster Anions TaC n- ( n = 1-4) with Dinitrogen

Dinitrogen activation/fixation is one of the most important and challenging subjects in synthetic as well as theoretical chemistry. In this study, the adsorption reactions of N₂ onto TaC _n^- ( n = 1-4) cluster anions have been investigated by means of mass spectrometry in conjunction with density functional theory calculations. Following the experimental results that only TaC₄^- was observed to adsorb N₂, theoretical calculations predicted that the TaC₄^- reaction system (TaC₄^- + N₂ → TaC₄N₂^-) has a negligible barrier on the approach of N₂ molecule while insurmountable barriers are located on the reaction pathways of TaC_1-3^-/N₂ reaction systems. The natural bond orbital and molecular orbital analysis indicated that the more positive charge on the metal center of TaC_1-4^- would facilitate the initial approach of the nonpolar N₂ molecule, and the appropriate frontier orbital of TaC_1-4^- with proper symmetry (π-type 5d orbital) which can match up well with the π* antibonding orbital of the N₂ molecule with less σ repulsion and more possibility for π back-donation would be helpful for the formation of the stable encounter complexes. This study reveals the fundamental rules and key factors governing the N₂ adsorption.

The role of spin states in the catalytic mechanism of the intra- and extradiol cleavage of catechols by O2

Iron-dependent enzymes and biomimetic iron complexes can catalyze the ring cleavage of very inert, aromatic compounds. The mechanisms of these transformations and the factors that lead either to extradiol cleavage or intradiol cleavage have not been fully understood. By using density functional theory we have elucidated the mechanism of the catalytic cycle for two biomimetic complexes, and explained the difference in the experimentally obtained products.

Assessment of electronic structure methods for the determination of the ground spin states of Fe(ii), Fe(iii) and Fe(iv) complexes

We studied spin states of Fe²⁺ ion, gaseous FeO, and 14 Fe(ii), Fe(iii) and Fe(iv) complexes using density functional theory.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

Molecular and Interfacial Calculations of Iron(II) Light Harvesters

Iron-carbene complexes show considerable promise as earth-abundant light-harvesters, and adsorption onto nanostructured TiO2 is a crucial step for developing solar energy applications. Intrinsic electron injection capabilities of such promising Fe(II) N-heterocyclic complexes (Fe-NHC) to TiO2 are calculated here, and found to correlate well with recent experimental findings of highly efficient interfacial injection. First, we examine the special bonding characteristics of Fe-NHC light harvesters. The excited-state surfaces are examined using density functional theory (DFT) and time-dependent DFT (TD-DFT) to explore relaxed excited-state properties. Finally, by relaxing an Fe-NHC adsorbed on a TiO2 nanocluster, we show favorable injection properties in terms of interfacial energy level alignment and electronic coupling suitable for efficient electron injection of excited electrons from the Fe complex into the TiO2 conduction band on ∼100 fs time scales.

Theoretical Study of Spin Crossover in 30 Iron Complexes

Iron complexes are important spin crossover (SCO) systems with vital roles in oxidative metabolism and promising technological potential. The SCO tendency depends on the free energy balance of high- and low-spin states, which again depends on physical effects such as dispersion, relativistic effects, and vibrational entropy. This work studied 30 different iron SCO systems with experimentally known thermochemical data, using 12 different density functionals. Remarkably general entropy-enthalpy compensation across SCO systems was identified (R = 0.82, p = 0.002) that should be considered in rational SCO design. Iron(II) complexes displayed higher ΔH and ΔS values than iron(III) complexes and also less steep compensation effects. First-coordination sphere ΔS values computed from numerical frequencies reproduce most of the experimental entropy and should thus be included when modeling spin-state changes in inorganic chemistry (R = 0.52, p = 3.4 × 10(-3); standard error in TΔS ≈ 4.4 kJ/mol at 298 K vs 16 kJ/mol of total TΔS on average). Zero-point energies favored high-spin states by 9 kJ/mol on average. Interestingly, dispersion effects are surprisingly large for the SCO process (average: 9 kJ/mol, but up to 33 kJ/mol) and favor the more compact low-spin state. Relativistic effects favor low-spin by ∼9 kJ/mol on average, but up to 24 kJ/mol. B3LYP*, TPSSh, B2PLYP, and PW6B95 performed best for the typical calculation scheme that includes ZPE. However, if relativistic and dispersion effects are included, only B3LYP* remained accurate. On average, high-spin was favored by LYP by 11-15 kJ/mol relative to other correlation functionals, and by 4.2 kJ/mol per 1% HF exchange in hybrids. 13% HF exchange was optimal without dispersion, and 15% was optimal with all effects included for these systems.

Density-Functional Theory Investigation of the Geometric, Energetic, and Optical Properties of the Cobalt(II)tris(2,2'-bipyridine) Complex in the High-Spin and the Jahn-Teller Active Low-Spin States

State-of-the-art generalized gradient approximation (GGA) (PBE, OPBE, RPBE, OLYP, and HCTH), meta-GGA (VSXC and TPSS), and hybrid (B3LYP, B3LYP*, O3LYP, and PBE0) functionals are compared for the determination of the structure and the energetics of the D3 [Co(bpy)3](2+) complex in the (4)A2 and (4)E trigonal components of the high-spin (4)T1g([Formula: see text]  [Formula: see text] ) state and in the low-spin (2)E state of octahedral (2)Eg([Formula: see text]  [Formula: see text] ) parentage. Their comparison extends also to the investigation of the Jahn-Teller instability of the (2)E state through the characterization of the extrema of C2 symmetry of this spin state's potential energy surface. The results obtained for [Co(bpy)3](2+) in either spin manifold are very consistent among the functionals used and are in good agreement with available experimental data. The functionals, however, perform very differently with respect to the spin-state energetics because the calculated values of the high-spin/low-spin energy difference Δ[Formula: see text] vary between -3212 and 3919 cm(-)(1). Semilocal functionals tend to give too large Δ[Formula: see text] values and thus fail to correctly predict the high-spin state as the ground state of the isolated complex, while hybrid functionals tend to overestimate the stability of the high-spin state with respect to the low-spin state. Reliable results are, however, obtained with the OLYP, HCTH, B3LYP*, and O3LYP functionals which perform best for the description of the isolated complex. The optical properties of [Co(bpy)3](2+) in the two spin states are also analyzed on the basis of electronic excitation calculations performed within time-dependent density functional response theory. The calculated absorption and circular dichroism spectra agree well with experimental results.

Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co(III)(diiminato)(NPh)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

Optimized Finite Difference Method for the Full-Potential XANES Simulations: Application to Molecular Adsorption Geometries in MOFs and Metal-Ligand Intersystem Crossing Transients

Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal-organic frameworks and (ii) light induced dynamics of spin crossover in metal-organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni-CO configuration was found to be linear, while Ni-NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)3](2+) with a 100 ps delay we identified the Fe-N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.