DFT Computation of Relative Spin-State Energetics of Transition Metal Compounds

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

Two-State Hydrogen Atom Transfer Reactivity of Unsymmetric [Cu2(O)(NO)]2+ Complexes

We report the temperature-dependent spin switching of dicopper oxo nitrosyl [Cu2(O)(NO)]2+ complexes and their influence on hydrogen atom transfer (HAT) reactivity. Electron paramagnetic resonance (EPR) and Evans method analysis suggest that [Cu2(O)(NO)]2+ complexes transition from the S = 1/2 to the S = 3/2 state around ca. 202 K. At low temperatures (198 K) where S = 3/2 dominates, a strong correlation between the rate of HAT (kHAT) and the population of the S = 1/2 state was identified (R2 = 0.988), suggesting that the HAT by [Cu2(O)(NO)]2+ complexes proceeds by the S = 1/2 isomer. Installation of functional groups that introduce an unsymmetric secondary coordination environment accelerates the HAT rates through perturbation of the spin equilibria. Given the often unsymmetric coordination sphere of bimetallic active sites in natural proteins, we anticipate that similar strategies could be employed by metalloenzymes to control HAT reactions.

Photodissociation Spectroscopy and Photofragment Imaging of the Fe+(Acetylene) Complex

Tunable laser photodissociation spectroscopy in the 700-400 nm region and photofragment imaging experiments are employed to investigate the Fe⁺(acetylene) ion-molecule complex. At energies above a threshold at 679 nm, continuous dissociation is detected throughout the visible wavelength region, with regions of broad structure. Comparison to the spectrum predicted by time-dependent density functional theory (TD-DFT) indicates that the complex has a quartet ground state. The dissociation threshold for Fe⁺(acetylene) at 679 nm provides the dissociation energy on the quartet potential energy surface. Correction for the atomic quartet-sextet spin state energy difference provides an adiabatic dissociation energy of 36.8 ± 0.2 kcal/mol. Photofragment imaging of the Fe⁺ photoproduct produced at 603.5 nm produces significant kinetic energy release (KER). The photon energy and the maximum value of the KER provide an upper limit on the dissociation energy of D₀ ≤ 34.6 ± 3.2 kcal/mol. The dissociation energies determined from the spectroscopy and photofragment imaging experiments agree nicely with the value determined previously by collision-induced dissociation (38.0 ± 2.6 kcal/mol). However, both values are significantly lower than those produced by computational chemistry at the DFT level using different functionals recommended for transition-metal chemistry.

Coordination and Spin States in Fe+(C2H2)n Complexes Studied with Selected-Ion Infrared Spectroscopy

Fe⁺(acetylene)_n ion-molecule complexes are produced in a supersonic molecular beam with pulsed laser vaporization. These ions are mass selected and studied with infrared photodissociation spectroscopy in the C-H stretching region, complemented by computational chemistry calculations. All C-H stretch vibrations are shifted to frequencies lower than the vibrations of isolated acetylene because of the charge transfer that occurs between the metal ion and the molecules. Complexes in the size range of n = 1-4 are found to have structures with individual acetylene molecules bound to the core metal ion via cation-π interactions. The coordination is completed with four ligands in a structure close to a distorted tetrahedron. Larger complexes in the range of n = 5-8 have external acetylene molecules solvating this n = 4 core ion via CH-π bonding to inner-shell ligands. DFT computations predict that quartet spin states are more stable for all complex sizes, but infrared spectra for quartet and doublet spin states are quite similar, precluding definitive determination of the spin states. There is no evidence for any of these complexes having acetylenes coupled into reacted structures. This is consistent with computed thermochemistry, which finds significant activation barriers to such reactions.

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.

Photoinduced Charge Transfer in the Zn-Methanol Cation Studied with Selected-Ion Photofragment Imaging

The Zn+(methanol) ion molecule complex produced by laser vaporization is studied with photofragment imaging at 280 and 266 nm. Photodissociation produces the methanol cation CH3OH+ via excitation of a charge-transfer excited state. Surprisingly, excitation of bound excited states produces the same fragment via a curve crossing prior to separation of products. Significant kinetic energy release is detected at both wavelengths with isotropic angular distributions. Similar experiments are conducted on the perdeuterated methanol complex. The Zn+ cation is a minor product channel that also exhibits significant kinetic energy release. An energetic cycle using the ionization potentials of zinc and methanol together with the kinetic energy release produces an upper limit on the Zn+-methanol bond energy of 33.7 {plus minus} 4.2 kcal/mol (1.46 {plus minus} 0.18 eV).

Chemoton 2.0: Autonomous Exploration of Chemical Reaction Networks

Fueled by advances in hardware and algorithm design, large-scale automated explorations of chemical reaction space have become possible. Here, we present our approach to an open-source, extensible framework for explorations of chemical reaction mechanisms based on the first-principles of quantum mechanics. It is intended to facilitate reaction network explorations for diverse chemical problems with a wide range of goals such as mechanism elucidation, reaction path optimization, retrosynthetic path validation, reagent design, and microkinetic modeling. The stringent first-principles basis of all algorithms in our framework is key for the general applicability that avoids any restrictions to specific chemical systems. Such an agile framework requires multiple specialized software components of which we present three modules in this work. The key module, Chemoton, drives the exploration of reaction networks. For the exploration itself, we introduce two new algorithms for elementary-step searches that are based on Newton trajectories. The performance of these algorithms is assessed for a variety of reactions characterized by a broad chemical diversity in terms of bonding patterns and chemical elements. Chemoton successfully recovers the vast majority of these. We provide the resulting data, including large numbers of reactions that were not included in our reference set, to be used as a starting point for further explorations and for future reference.

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.

Computational Investigation of the Metal and Ligand Substitution Effects on the Structure and Electronic States of the Phosphoranimide Tetramer Complexes of Cu(I), Ni(I), Co(I), and Fe(I)

The structurally unique saddle-shaped paramagnetic tetrametallic clusters of Co(I) and Ni(I) with phosphoranimide ligands have been synthesized and proposed as catalyst precursors. The analogous Cu(I) nanocluster is planar and diamagnetic. These notable variations in geometry and ground electronic states indicate that the effect of metal and ligand substituents on the structure and electronic properties of these complexes requires investigation. We present a computational study of a series of these novel homoleptic complexes containing Co(I), Ni(I), and Cu(I) as well as Fe(I) coordinated to phosphoranimides with electron-donating and withdrawing substituents, conducted at the relativistic density functional theory level using ZORA-PBE/TZP. The optimized structures of the saddle-shaped Co(I) and Ni(I) and planar Cu(I) tetramers with linear N-M-N coordination are validated with respect to X-ray diffraction determinations. The ground-state analysis indicates that Cu(I) complexes are diamagnetic, whereas Ni(I) and Co(I) complexes are in high-spin states, in agreement with magnetic susceptibility measurements. The computational results show that Fe(I) complexes are saddle shaped and high spin. The Co(I) complex is stabilized by a metal macrocycle distortion from square to diamond, as elucidated from its Walsh diagram. The effects of metals and ligand substituents on the ground electronic state, metal center coordination environment, and energy of the complexes are investigated. The bulky tertiary butyl substituent causes the largest saddle-shape distortion of the tetramer marcocycle, which partially offsets its electron-donating effect. Macrocycle distortions with N-M-N site angles ranging from obtuse to alternating obtuse reflex are correlated with the increasing number of unpaired electrons. The phenyl-substituted complexes are expected to have the highest reactivity toward electrophiles. Understanding the interplay between structural and electronic parameters is intended to guide the development of synthetic cooperative systems for multielectron redox reactions, models of biological systems, and molecular magnets.

Generation of Highly Vibrationally Excited CO in Sequential Photodissociation of Iron Carbonyl Complexes

Ultraviolet photochemistry of iron pentacarbonyl, Fe(CO)₅, was investigated with resonantly enhanced multiphoton ionization (REMPI) spectroscopy and ion imaging. The REMPI spectrum of CO photofragments, generated by ultraviolet irradiation of Fe(CO)₅, showed the generation in the highly vibrationally excited states with v = 11-15. Analysis of the band intensities observed in the 213-235 nm region indicated that the high-v CO generation was maximized at around 220 nm. Generation yields of the coordinatively unsaturated intermediates, Fe(CO)_n=1-4, were measured as a function of the photolysis wavelength using a nonresonant detection scheme. The yield spectrum of FeCO was correlated with that of the high-v CO fragments, suggesting high-v CO generation in the photodissociation of FeCO. The density functional theory calculations of the excited states of FeCO showed an intense photoabsorption to the metal-centered state near 220 nm. The theoretical results were consistent with the interpretation of FeCO + hν → Fe + high-v CO, which was experimentally indicated. The momentum distribution obtained from the velocity distributions of Fe, Fe(CO)₄, and CO fragments further supported that Fe is the counter-product of the high-v CO fragment. The present results provided selective observation of the photochemistry of the unsaturated iron carbonyl complexes, which has not been well elucidated in laser-based experiments because of the uncontrollable sequential photodissociation producing mixed Fe(CO)_n intermediates.

A DMRG/CASPT2 Investigation of Metallocorroles: Quantifying Ligand Noninnocence in Archetypal 3d and 4d Element Derivatives

Hybrid density functional theory (B3LYP) and density matrix renormalization group (DMRG) theory have been used to quantitatively compare the degree of ligand noninnocence (corrole radical character) in seven archetypal metallocorroles. The seven complexes, in decreasing order of corrole noninnocent character, are Mn[Cor]Cl > Fe[Cor]Cl > Fe[Cor](NO) > Mo[Cor]Cl2 > Ru[Cor](NO) ≈ Mn[Cor]Ph ≈ Fe[Cor]Ph ≈ 0, where [Cor] refers to the unsubstituted corrolato ligand. DMRG-based second-order perturbation theory calculations have also yielded detailed excited-state energetics data on the compounds, shedding light on periodic trends involving middle transition elements. Thus, whereas the ground state of Fe[Cor](NO) (S = 0) is best described as a locally S = 1/2 {FeNO}7 unit antiferromagnetically coupled to a corrole A' radical, the calculations confirm that Ru[Cor](NO) may be described as simply {RuNO}6-Cor3-, that is, having an innocent corrole macrocycle. Furthermore, whereas the ferromagnetically coupled S = 1{FeNO}7-Cor•2- state of Fe[Cor](NO) is only ∼17.5 kcal/mol higher than the S = 0 ground state, the analogous triplet state of Ru[Cor](NO) is higher by a far larger margin (37.4 kcal/mol) relative to the ground state. In the same vein, Mo[Cor]Cl2 exhibits an adiabatic doublet-quartet gap of 36.1 kcal/mol. The large energy gaps associated with metal-ligand spin coupling in Ru[Cor](NO) and Mo[Cor]Cl2 reflect the much greater covalent character of 4d-π interactions relative to analogous interactions involving 3d orbitals. As far as excited-state energetics is concerned, DMRG-CASPT2 calculations provide moderate validation for hybrid density functional theory (B3LYP) for qualitative purposes, but underscore the possibility of large errors (>10 kcal/mol) in interstate energy differences.

Redox Isomerism in the S3 State of the Oxygen-Evolving Complex Resolved by Coupled Cluster Theory

The electronic and geometric structures of the water-oxidizing complex of photosystem II in the steps of the catalytic cycle that precede dioxygen evolution remain hotly debated. Recent structural and spectroscopic investigations support contradictory redox formulations for the active-site Mn4 CaOx cofactor in the final metastable S3 state. These range from the widely accepted MnIV 4 oxo-hydroxo model, which presumes that O-O bond formation occurs in the ultimate transient intermediate (S4 ) of the catalytic cycle, to a MnIII 2 MnIV 2 peroxo model representative of the contrasting "early-onset" O-O bond formation hypothesis. Density functional theory energetics of suggested S3 redox isomers are inconclusive because of extreme functional dependence. Here, we use the power of the domain-based local pair natural orbital approach to coupled cluster theory, DLPNO-CCSD(T), to present the first correlated wave function theory calculations of relative stabilities for distinct redox-isomeric forms of the S3 state. Our results enabled us to evaluate conflicting models for the S3 state of the oxygen-evolving complex (OEC) and to quantify the accuracy of lower-level theoretical approaches. Our assessment of the relevance of distinct redox-isomeric forms for the mechanism of biological water oxidation strongly disfavors the scenario of early-onset O-O formation advanced by literal interpretations of certain crystallographic models. This work serves as a case study in the application of modern coupled cluster implementations to redox isomerism problems in oligonuclear transition metal systems.

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.

Infrared photodissociation spectroscopy of heteronuclear group 15 metal-iron carbonyl cluster anions AmFe(CO)n- (A = Sb, Bi; m, n = 2, 3)

Heteronuclear group 15 metal-iron carbonyl cluster complexes of A_mFe(CO)_n^- (A = Sb, Bi; m, n = 2-3) were generated in the gas phase and studied by infrared photodissociation spectroscopy in the carbonyl stretching region. Their structures were determined by comparing the experimental spectra with predicted spectra derived from DFT calculations at the B3LYP and BP86 levels. All of the A_mFe(CO)_n^- cluster anions were determined to have Fe(CO)_n^- fragments with all of the CO ligands terminally bonded to the iron center, and they can be regarded as being formed via the interactions of the neutral group 15 metal clusters with the Fe(CO)_n^- fragments. Bonding analyses indicated that each A₂Fe(CO)_n^- (n = 2, 3) cluster anion contained two A-Fe single bonds and one A-A double bond. Each A₃Fe(CO)_n^- (n = 2, 3) cluster anion involved three A-Fe single bonds and three A-A single bonds. There is an isolobal relationship between the Fe(CO)₃^- group and the group 15 atoms. The substitution of an Fe(CO)₃^- group in place of one A atom in the tetrahedral A₄ molecule resulted in an A₃Fe(CO)₃^- cluster anion with the closed-shell electronic configuration for all the group 15 metals and iron atoms.

Gold nanoclusters as prospective carriers and detectors of pramipexole

Pramipexole (PPX) is known in the treatment of Parkinson's disease and restless legs syndrome. We carried out a theoretical investigation on pramipexole-Au cluster interactions for the applications of drug delivery and detection. Three Au N clusters with sizes N = 6, 8 and 20 were used as reactant models to simulate the metallic nanostructured surfaces. Quantum chemical computations were performed in both gas phase and aqueous environments using density functional theory (DFT) with the PBE functional and the cc-pVDZ-PP/cc-pVTZ basis set. The PPX drug is mainly adsorbed on gold clusters via its nitrogen atom of the thiazole ring with binding energies of ca. -22 to -28 kcal mol-1 in vacuum and ca. -18 to -24 kcal mol-1 in aqueous solution. In addition to such Au-N covalent bonding, the metal-drug interactions are further stabilized by electrostatic effects, namely hydrogen-bond NH⋯Au contributions. Surface-enhanced Raman scattering (SERS) of PPX adsorbed on the Au surfaces and its desorption process were also examined. In comparison to Au8, both Au6 and Au20 clusters undergo a shorter recovery time and a larger change of energy gap, being possibly conducive to electrical conversion, thus signaling for detection of the drug. A chemical enhancement mechanism for SERS procedure was again established in view of the formation of nonconventional hydrogen interactions Au⋯H-N. The binding of PPX to a gold cluster is expected to be reversible and triggered by the presence of cysteine residues in protein matrices or lower-shifted alteration of environment pH. These findings would encourage either further theoretical probes to reach more accurate views on the efficiency of pramipexole-Au interactions, or experimental attempts to build appropriate gold nanostructures for practical trials, harnessing their potentiality for applications.

Ultraviolet photodissociation of gas-phase iron pentacarbonyl probed with ultrafast infrared spectroscopy

It is well known that ultraviolet photoexcitation of iron pentacarbonyl results in rapid loss of carbonyl ligands leading to the formation of coordinatively unsaturated iron carbonyl compounds. We employ ultrafast mid-infrared transient absorption spectroscopy to probe the photodissociation dynamics of gas-phase iron pentacarbonyl following ultraviolet excitation at 265 and 199 nm. After photoexcitation at 265 nm, our results show evidence for sequential dissociation of iron pentacarbonyl to form iron tricarbonyl via a short-lived iron tetracarbonyl intermediate. Photodissociation at 199 nm results in the prompt production of Fe(CO)₃ within 0.25 ps via several energetically accessible pathways. An additional 15 ps time constant extracted from the data is tentatively assigned to intersystem crossing to the triplet manifold of iron tricarbonyl or iron dicarbonyl. Mechanisms for formation of iron tetracarbonyl, iron tricarbonyl, and iron dicarbonyl are proposed and theoretically validated with one-dimensional cuts through the potential energy surface as well as bond dissociation energies. Ground state calculations are computed at the CCSD(T) level of theory and excited states are computed with EOM-EE-CCSD(dT).

Widening the Window of Spin-Crossover Temperatures in Bis(formazanate)iron(II) Complexes via Steric and Noncovalent Interactions

Bis(formazanate)iron(II) complexes undergo a thermally induced S = 0 to S = 2 spin transition in solution. Here we present a study of how steric effects and π-stacking interactions between the triarylformazanate ligands affect the spin-crossover behavior, in addition to electronic substituent effects. Moreover, the effect of increasing the denticity of the formazanate ligands is explored by including additional OMe donors in the ligand (7). In total, six new compounds (2–7) have been synthesized and characterized, both in solution and in the solid state, via spectroscopic, magnetic, and structural analyses. The series spans a broad range of spin-crossover temperatures (T_1/2) for the LS ⇌ HS equilibrium in solution, with the exception of compound 6 which remains high-spin (S = 2) down to 210 K. In the solid state, 6 was shown to exist in two distinct forms: a tetrahedral high-spin complex (6a, S = 2) and a rare square-planar structure with an intermediate-spin state (6b, S = 1). SQUID measurements, ⁵⁷Fe Mössbauer spectroscopy, and differential scanning calorimetry indicate that in the solid state the square-planar form 6b undergoes an incomplete spin-change-coupled isomerization to tetrahedral 6a. The complex that contains additional OMe donors (7) results in a six-coordinate (NNO)₂Fe coordination geometry, which shifts the spin-crossover to significantly higher temperatures (T_1/2 = 444 K). The available experimental and computational data for 7 suggest that the Fe···OMe interaction is retained upon spin-crossover. Despite the difference in coordination environment, the weak OMe donors do not significantly alter the electronic structure or ligand-field splitting, and the occurrence of spin-crossover (similar to the compounds lacking the OMe groups) originates from a large degree of metal–ligand π-covalency.

A series of Fe(II) complexes with formazanate ligands are reported, and ligand substituent effects on structure and spin-crossover properties are examined. These ligand modifications allow isolation of compounds with tetrahedral geometries in both low- and high-spin ground states as well as an intermediate-spin square-planar complex. Steric properties, π-stacking interactions, and additional donor substituents lead to a wide range of spin-crossover temperatures (T_1/2) in this class of compounds.

Spin-state dependence of exchange-correlation holes

Applications of density-functional theory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations feature such an explicit spin-state dependence [C. R. Jacob and M. Reiher, Int. J. Quantum Chem., 2012, 112, 3661-3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.

Cation-π Complexes of Silver Studied with Photodissociation and Velocity-Map Imaging

Ag⁺(aromatic) ion-molecule complexes of benzene, toluene, or furan are generated in the gas phase by laser vaporization in a supersonic expansion. These ions are mass selected in a time-of-flight spectrometer and studied with ultraviolet laser photodissociation and photofragment imaging. UV laser excitation results in dissociative charge transfer (DCT) for these ions, producing neutral silver atom and the respective aromatic cation as the photofragments. Velocity-map imaging and slice imaging techniques are employed to investigate the kinetic energy release in these photodissociation processes. In each case, DCT produces significant kinetic energy, and evidence is also found for excitation of the internal rovibrational degrees of freedom for the molecular cations. Analysis of the kinetic energy release together with the known ionization energies of silver and the molecular ligands provides new information on the cation-π bond energies.

Elucidating the binding mechanism of thione-containing mercaptopurine and thioguanine drugs to small gold clusters

Density functional theory methods were employed to clarify the adsorption/desorption behaviors of the thione-containing mercaptopurine and thioguanine drugs on the gold surface using both small Au₆ and Au₈ clusters as model reactants. Structural features, thermodynamic parameters, bonding characteristics, and electronic properties of the resulting complexes were investigated using the Perdew-Burke-Ernzerhof (PBE) and LC-BLYP functionals along with correlation-consistent basis sets, namely cc-pVDZ-PP for gold and cc-pVTZ for non-metals. Computed results show that the drug molecules tend to anchor on the gold cluster at the S atom with binding energies around -34 to -40 kcal/mol (in vacuum) and - 28 to -32 kcal/mol (in aqueous solution). As compared to Au₈ , Au₆ undergoes a shorter recovery time and a larger change of energy gap that could be converted to an electrical signal for selective detection of the drugs. Furthermore, interactions between the drugs and gold clusters are reversible processes and a drug release mechanism was also proposed. Accordingly, the drugs are able to separate from the gold surface due to either a slight change of pH in tumor cells or the presence of cysteine residues in protein matrices.

A family of lead clusters with precious metal cores

Gold nanoparticles have been used for centuries, both for decoration and in medical applications. More recently, many of the major advances in cluster chemistry have involved well-defined clusters containing tens or hundreds of atoms, either with or without a ligand shell. In this paper we report the synthesis of two gold/lead clusters, [Au₈Pb₃₃]⁶⁻ and [Au₁₂Pb₄₄]⁸⁻, both of which contain nido [Au@Pb₁₁]³⁻ icosahedra surrounding a core of Au atoms. Analogues of these large clusters are not found in the corresponding Ag chemistry: instead, the Ag-centered nido icosahedron, [Ag@Pb₁₁]³⁻, is the only isolated product. The structural chemistry, along with the mass spectrometry which shows the existence of [Au₂Pb₁₁]²⁻ but not [Ag₂Pb₁₁]²⁻, leads us to propose that the former species is the key intermediate in the growth of the larger clusters. Density functional theory indicates that secondary π-type interactions between the [Au@Pb₁₁]³⁻ ligands and the gold core play a significant part in stabilizing the larger clusters.

Many Zintl ions with a single endohedrally encapsulated transition metal ion are known, but relatively few where clusters of two or more metals are present. Here, the authors report the synthesis and characterization of two clusters, [Au₈Pb₃₃]⁶⁻ and [Au₁₂Pb₄₄]¹²⁻, which contain Au₈ and Au₁₂ cores surrounded by Pb shells.

Structural Evolution and Stability Trend of Small-Sized Gold Clusters Aun (n = 20-30)

Structural evolution and stability pattern of pure neutral gold clusters Au_n in the small size range of n = 20-30 are examined using density functional theory (DFT) calculations. The equilibrium geometries are either confirmed or determined, and some new ground state structures are identified. The most stable configurations of Au₂₁-Au₂₃ sizes are formed by adding extra gold atoms to the highly stable pyramidal structure of Au₂₀, while flat-cage shapes are the best candidates for the global minima of both Au₂₄ and Au₂₅. For larger sizes of n = 26-30, pyramidal motifs tend to dominate the lower-lying population rather than tubular conformations as previously reported. The energy gaps, excitation energies, and exciton binding energies are also computed to test out the performance of the computational methods employed. Accordingly, a density functional with long-range exchange effects is highly recommended to quantitatively investigate both the ground and excited states of pure gold clusters.

Microsolvation in V+(H2O)n Clusters Studied with Selected-Ion Infrared Spectroscopy

Gas-phase ion-molecule clusters of the form V⁺(H₂O)_n (n = 1-30) are produced by laser vaporization in a supersonic expansion. These ions are analyzed and mass-selected with a time-of-flight mass spectrometer and investigated with infrared laser photodissociation spectroscopy. The small clusters (n ≤ 7) are studied with argon tagging, while the larger clusters are studied via the elimination of water molecules. The vibrational spectra for the small clusters include only free O-H stretching vibrations, while larger clusters exhibit redshifted hydrogen bonding vibrations. The spectral patterns reveal that the coordination around V⁺ ions is completed with four water molecules. A symmetric square-planar structure forms for the n = 4 ion, and this becomes the core ion in larger structures. Clusters up to n = 8 have mostly two-dimensional structures, but hydrogen bonding networks evolve to three-dimensional structures in larger clusters. The free O-H vibration of acceptor-acceptor-donor (AAD)-coordinated surface molecules converges to a frequency near that of bulk water by the cluster size of n = 30. However, the splitting of this vibration for AAD- versus AD-coordinated molecules is still different compared to other singly charged or doubly charged cation-water clusters. This indicates that cation identity and charge-site location in the cluster can produce discernable spectral differences for clusters in this size range.

The Irony of Manganocene: An Interplay between the Jahn-Teller Effect and Close-Lying Electronic and Spin States

Although the unusual structural, magnetic, electronic, and spin characteristics of manganocene has intrigued scientists for decades, a unified explanation and rationalization of its properties has not yet been provided. Results obtained by Multideterminantal Density Functional Theory (MD-DFT), Energy Decomposition Analysis (EDA), and Intrinsic Distortion Path (IDP) methodologies indicate how this uniqueness can be traced back to the manganocene's peculiar electronic structure, mainly, the degenerate ground state and close-lying electronic and spin states.

Limits of Coupled-Cluster Calculations for Non-Heme Iron Complexes

In a large variety of studies, the coupled-cluster method with singles, doubles, and perturbative triples (CCSD(T)) is used as a reference for benchmarking the performance of density functional theory (DFT) functionals. In the case of open-shell species, this theory can be applied in different forms depending on the restricted or unrestricted treatment of spin. In this study, we show that these different approaches can produce results which deviate by ∼5 kcal/mol for different species on the potential energy surfaces. This was demonstrated for a simple model of the C-H activation carried out by non-heme iron enzymes. Assessing the limits of CCSD(T) prior to its use as a general benchmark tool is warranted. This was done using higher-order coupled-cluster calculations as well as multiconfigurational second-order perturbation theory (CASPT2), since iron-oxo species present some multireference character. Furthermore, we tested two different implementations of the local coupled-cluster method and compared them to the CCSD(T) results, showing that even though these novel approaches are promising, without further developments they appear not to be suitable for describing two-state reactivity of the system investigated in the current study. Additionally, we implemented and assessed the performance of the hotspot approach for the local unrestricted CCSD(T) scheme which aims at reducing the pair error for systems containing transition metals.

Higher spin states in some low-energy bis(tetramethyl-1,2-diaza-3,5-diborolyl) sandwich compounds of the first row transition metals: boraza analogues of the metallocenes

Density functional studies on (Me₄B₂N₂CH)₂M (M = Ti, V, Cr, Mn, Fe, Co, Ni) show low-energy sandwich structures for all seven metals. The lowest-energy such Cr and Mn derivatives have higher spin states than the corresponding metallocenes.

Computational Methods for Modeling Metalloproteins

Metalloproteins are challenging objects if we want to investigate their chemical reactivity with theoretical approaches such as density functional theory (DFT). The complexity of these biomolecules often requires us to find a compromise between accuracy and feasibility, one that is tailored to the questions we set out to answer. In this chapter, we discuss computational approaches to studying chemical reactions in metalloproteins and how to utilize the information hidden in homologous proteins.

Probing the Valence Electronic Structure of Low-Spin Ferrous and Ferric Complexes Using 2p3d Resonant Inelastic X-ray Scattering (RIXS)

Understanding the detailed electronic structure of transition metal ions is essential in numerous areas of inorganic chemistry. In particular, the ability to map out the many particle d-d spectrum of a transition metal catalyst is key to understanding and predicting reactivity. However, from a practical perspective, there are often experimental limitations on the ability to determine the energetic ordering, and multiplicity of all the excited states. These limitations derive in part from parity and spin-selection rules, as well as from the limited energy range of many standard laboratory instruments. Herein, we demonstrate the ability of 2p3d resonant inelastic X-ray scattering (RIXS) to obtain detailed insights into the many particle spectrum of simple inorganic molecular iron complexes. The present study focuses on low-spin ferrous and ferric iron complexes, including [Fe^III/II(tacn)₂]^3+/2+ and [Fe^III/II(CN)₆]^3-/4-. This series thus allows us to assess the contribution of d-count and ligand donor type, by comparing the purely σ-donating tacn ligand to the π-accepting cyanide. In order to highlight the conceptual difference between RIXS and traditional optical spectroscopy, we compare first RIXS results with UV-vis and magnetic circular dichroism spectroscopy. We then highlight the ability of 2p3d RIXS to (1) separate d-d transitions from charge transfer transitions and (2) to determine the many particle d-d spectrum over a much wider energy range than is possible by optical spectroscopy. Our experimental results are correlated with semiempirical multiplet simulations and ab initio complete active space self-consistent field calculations in order to obtain detailed assignments of the excited states. These results show that Δ S = 1, and possibly Δ S = 2, transitions may be observed in 2p3d RIXS spectra. Hence, this methodology has great promise for future applications in all areas of transition metal inorganic chemistry.

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.

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.