Modeling Fe(II) Complexes Using Neural Networks

We report a Fe(II) data set of more than 23000 conformers in both low-spin (LS) and high-spin (HS) states. This data set was generated to develop a neural network model that is capable of predicting the energy and the energy splitting as a function of the conformation of a Fe(II) organometallic complex. In order to achieve this, we propose a type of scaled electronic embedding to cover the long-range interactions implicitly in our neural network describing the Fe(II) organometallic complexes. For the total energy prediction, the lowest MAE is 0.037 eV, while the lowest MAE of the splitting energy is 0.030 eV. Compared to baseline models, which only incorporate short-range interactions, our scaled electronic embeddings improve the accuracy by over 70% for the prediction of the total energy and the splitting energy. With regard to semiempirical methods, our proposed models reduce the MAE, with respect to these methods, by 2 orders of magnitude.

Transition Temperature for Spin-Crossover Materials with the Mean Value Ensemble Hubbard-U Correction

Calculation of transition temperatures T1/2 for thermally driven spin-crossover in condensed phases is challenging, even with sophisticated state-of-the-art density functional approximations. The first issue is the accuracy of the adiabatic crossover energy difference ΔEHL between the low- and high-spin states of the bistable metal-organic complexes. The other is the proper inclusion of entropic contributions to the Gibbs free energy from the electronic and vibrational degrees of freedom. We discuss the effects of treatments of both contributions upon the calculation of thermochemical properties for a set of 20 spin-crossover materials using a Hubbard-U correction obtained from a reference ensemble spin-state. The U values obtained from a simplest bimolecular representation may overcorrect, somewhat, the ΔEHL values, hence giving somewhat excessive reduction of the T1/2 results with respect to their U = 0 values in the crystalline phase. We discuss the origins of the discrepancies by analyzing different sources of uncertainties. By use of a first-coordination-sphere approximation and the assumption that vibrational contributions from the outermost atoms in a metal-organic complex are similar in both low- and high-spin states, we achieve T1/2 results with the low-cost, widely used PBE generalized gradient density functional approximation comparable to those from the more costly, more sophisticated r2SCAN meta-generalized gradient approximation. The procedure is promising for use in high-throughput materials screening, because it combines rather low computational effort requirements with freedom from user manipulation of parameters.

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2 (C2 H5 CN)2 ](BF4 )2 : Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties*

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄ )₂ ⋅6 H₂ O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂ (RCN)₂ ](BF₄ )₂ ⋅nRCN (n=2 for R=CH₃ (1) and n=0 for R=C₂ H₅ (2) C₃ H₇ (3), C₃ H₅ (4), CH₂ Cl (5)) exhibiting spin crossover (SCO). SCO in 1 and 3-5 is complete and occurs above 160 K. In 2, it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2 ^↓ =78 K, T_1/2 ^↑ =123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2. An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS -V_LS ) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe-nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂ (C₂ H₅ CN/C₃ H₇ CN)₂ ](BF₄ )₂ mixed crystals (2 a, 2 b), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1-5 suggest a particular possibility of 2 to adopt a low (140-145°) value of its Fe-N-C(propionitrile) angle.

Iron-Catalyzed Reductive Coupling of Alkyl Iodides with Alkynes To Yield cis-Olefins: Mechanistic Insights from Computation

In a recent study, a new procedure for Z-selective olefin synthesis by reductive coupling of alkyl iodides with terminal alkynes in the presence of iron salts is described. This transformation is representative of many newly developed synthetic routes through the involvement of multiple species and phases, which makes mechanistic insight hard to obtain. Here, we report computational work aimed at exploring the possible reaction pathways. DFT calculations lead to two suggested routes, one involving C-I reduction by metallic zinc and radical addition to the alkyne and the other involving addition of two reduced iron species to the alkyne bond followed by reductive elimination. Comparison to experimental results as well as kinetic modeling is used to discuss the likelihood of these and related mechanisms.

Observation of the First Spin Crossover in an Iron(II) Complex with an S6 Coordination Environment: Tris[bis(N,N-diethylamino)carbeniumdithiocarboxylato]iron(II) Hexafluorophosphate

For the first time, the spin-crossover (SCO) phenomenon has been observed in an Fe^II -S₆ system in a tris(chelate)-type iron(II) complex with a zwitterionic sulfur donor bidentate, bis(N,N-diethylamino)carbeniumdithiocarboxylate (EtL), [Fe^II (EtL)₃ ](PF₆ )₂ (1), as synthesized by the reaction of a precursor complex [Fe^II (CH₃ CN)₆ ](PF₆ )₂ with EtL. In the solid state, the high-spin (HS) d⁶ state at ambient temperature and the low-spin (LS) d⁶ state at temperatures lower than approximately 240 K were evidenced by magnetic measurements with SQUID and Mössbauer spectra in the temperature range 4-290 K. X-ray analyses of the crystals at various temperatures disclosed that the distorted trigonal prismatic coordination environments essentially do not change; however, contraction of Fe-S distances by approximately 10 % (0.22 Å), ordering of alkyl groups in EtL and PF₆ ^- counteranions, and formation of significant intermolecular S⋅⋅⋅S interactions between adjacent molecules (average distances of 3.59 Å) take place during the transition from the HS to the LS state. A large decrease in the volume of the formula unit (78.1 ų ) might be responsible for the large activation barrier, thereby resulting in a slow phase transition upon cooling.

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).

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.

Quantum chemical modeling of magnetically bistable metal coordination compounds. Synchronization of spin crossover, valence tautomerism and charge transfer induced spin transition mechanisms

Heterometallic complexes of 1,10-phenanthroline-5,6-dione exhibiting unprecedented dynamic behaviour due to synchronized thermally induced intramolecular rearrangements were computationally studied.

Abrupt versus Gradual Spin-Crossover in Fe(II)(phen)2(NCS)2 and Fe(III)(dedtc)3 Compared by X-ray Absorption and Emission Spectroscopy and Quantum-Chemical Calculations

Molecular spin-crossover (SCO) compounds are attractive for information storage and photovoltaic technologies. We compared two prototypic SCO compounds with Fe(II)N6 (1, [Fe(phen)2(NCS)2], with phen = 1,10-phenanthroline) or Fe(III)S6 (2, [Fe(dedtc)3], with dedtc = N,N'-diethyldithiocarbamate) centers, which show abrupt (1) or gradual (2) thermally induced SCO, using K-edge X-ray absorption and Kβ emission spectroscopy (XAS/XES) in a 8-315 K temperature range, single-crystal X-ray diffraction (XRD), and density functional theory (DFT). Core-to-valence and valence-to-core electronic transitions in the XAS/XES spectra and bond lengths change from XRD provided benchmark data, verifying the adequacy of the TPSSh/TZVP DFT approach for the description of low-spin (LS) and high-spin (HS) species. Determination of the spin densities, charge distributions, bonding descriptors, and valence-level configurations, as well as similar experimental and calculated enthalpy changes (ΔH), suggested that the varying metal-ligand bonding properties and deviating electronic structures converge to similar enthalpic contributions to the free-energy change (ΔG) and thus presumably are not decisive for the differing SCO behavior of 1 and 2. Rather, SCO seems to be governed by vibrational contributions to the entropy changes (ΔS) in both complexes. Intra- and intermolecular interactions in crystals of 1 and 2 were identified by atoms-in-molecules analysis. Thermal excitation of individual dedtc ligand vibrations accompanies the gradual SCO in 2. In contrast, extensive inter- and intramolecular phen/NCS vibrational mode coupling may be an important factor in the cooperative SCO behavior of 1.

Influence of conformational changes on spin crossover properties and superstructure formation in 2D coordination polymers [Fe(hbtz)2(RCN)2](ClO4)2

Spin-crossover, governed by conformational changes of nitrile molecule, triggers corrugation of polymeric skeleton and formation of superstructure in [Fe(hbtz)₂(allyl cyanide)₂](ClO₄)₂.

Halide binding and inhibition of laccase copper clusters: the role of reorganization energy

Laccase-like proteins are multicopper oxidases involved in several biological and industrial processes. Their application is commonly limited due to inhibition by fluoride and chloride, and as-isolated proteins are often substantially activated by heat, suggesting that multiple redox states can complicate characterization. Understanding these processes at the molecular level is thus desirable but theoretically unexplored. This paper reports systematic calculations of geometries, reorganization energies, and ionization energies for all partly oxidized states of the trinuclear copper clusters in realistic models with ∼200 atoms. Corrections for scalar-relativistic effects, dispersion, and thermal effects were estimated. Fluoride, chloride, hydroxide, or water was bound to the T2 copper site of the oxidized resting state, and the peroxo intermediate was also computed for reference. Antiferromagnetic coupling, assigned oxidation states, and general structures were consistent with known spectroscopic data. The computations show that (i) ligands bound to the T2 site substantially increase the reorganization energy of the second reduction of the resting state and reduce the redox potentials, providing a possible mechanism for inhibition; (ii) the reorganization energy is particularly large for F(-) but also high for Cl(-), consistent with the experimental tendency of inhibition; (iii) reduction leads to release of Cl(-) from the T2 site, suggesting a mechanism for heat/reduction activation of laccases by dissociation of inhibiting halides or hydroxide from T2.