Spin-Hamiltonian Parameters from First Principle Calculations: Theory and Application

Characterization of the active site in the thiocyanate-forming protein from Thlaspi arvense (TaTFP) using EPR spectroscopy

Glucosinolates are plant thioglucosides, which act as chemical defenses. Upon tissue damage, their myrosinase-catalyzed hydrolysis yields aglucones that rearrange to toxic isothiocyanates. Specifier proteins such as thiocyanate-forming protein from Thlaspi arvense (TaTFP) are non-heme iron proteins, which capture the aglucone to form alternative products, e.g. nitriles or thiocyanates. To resolve the electronic state of the bound iron cofactor in TaTFP, we applied continuous wave electron paramagnetic resonance (CW EPR) spectroscopy at X-and Q-band frequencies (∼9.4 and ∼34 GHz). We found characteristic features of high spin and low spin states of a d 5 electronic configuration and local rhombic symmetry during catalysis. We monitored the oxidation states of bound iron during conversion of allylglucosinolate by myrosinase and TaTFP in presence and absence of supplemented Fe2+. Without added Fe2+, most high spin features of bound Fe3+ were preserved, while different g'-values of the low spin part indicated slight rearrangements in the coordination sphere and/or structural geometry. We also examined involvement of the redox pair Fe3+/Fe2 in samples with supplemented Fe2+. The absence of any EPR signal related to Fe3+ or Fe2+ using an iron-binding deficient TaTFP variant allowed us to conclude that recorded EPR signals originated from the bound iron cofactor.

Nature of the Ligand-Centered Triplet State in Gd3+ β-Diketonate Complexes as Revealed by Time-Resolved EPR Spectroscopy and DFT Calculations

A series of Gd³⁺ complexes (Gd1–Gd3) with the general formula GdL₃(EtOH)₂, where L is a β-diketone ligand with polycyclic aromatic hydrocarbon substituents of increasing size (1–3), was studied by combining time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy and DFT calculations to rationalize the anomalous spectroscopic behavior of the bulkiest complex (Gd3) through the series. Its faint phosphorescence band is observed only at 80 K and it is strongly red-shifted (∼200 nm) from the intense fluorescence band. Moreover, the TR-EPR spectral analysis found that triplet levels of 3/Gd3 are effectively populated and have smaller |D| values than those of the other compounds. The combined use of zero-field splitting and spin density delocalization calculations, together with spin population analysis, allows us to explain both the large red shift and the low intensity of the phosphorescence band observed for Gd3. The large red shift is determined by the higher delocalization degree of the wavefunction, which implies a larger energy gap between the excited S₁ and T₁ states. The low intensity of the phosphorescence is due to the presence of C–H groups which favor non-radiative decay. These groups are present in all complexes; nevertheless, they have a relevant spin density only in Gd3. The spin population analysis on NaL models, in which Na⁺ is coordinated to a deprotonated ligand, mimicking the coordinative environment of the complex, confirms the outcomes on the free ligands.

A series of Gd³⁺ complexes (Gd1−Gd3) were studied by combining TR-EPR spectroscopy and DFT calculations to rationalize the deviant spectroscopic behavior of the bulkiest complex (Gd3). The combination of ZFS calculations and the spin density delocalization analysis ascribed the larger red shift to the higher degree of delocalization of the wavefunction and the low intensity of the phosphorescence band to the presence of C−H groups with relevant spin density that favor non-radiative decay.

One Electron Multiple Proton Transfer in Model Organic Donor-Acceptor Systems: Implications for High Frequency EPR

EPR spectroscopy is an important spectroscopic method for identification and characterization of radical species involved in many biological reactions. The tyrosyl radical is one of the most studied amino acid radical intermediates in biology. Often in conjunction with histidine residues, it is involved in many fundamental biological electron and proton transfer processes, such as in the water oxidation in photosystem II. As biological processes are typically extremely complicated and hard to control, molecular bio-mimetic model complexes are often used to clarify the mechanisms of the biological reactions. Here we present theoretical calculations to investigate the sensitivity of magnetic resonance parameters to proton-coupled electron transfer events, as well as conformational substates of the molecular constructs which mimic the tyrosine-histidine (Tyr-His) pairs found in a large variety of proteins. Upon oxidation of the phenol, the Tyr analogue, these complexes can perform not only one-electron one-proton transfer (EPT), but also one-electron two-proton transfers (E2PT). It is shown that in aprotic environment the g_X-components of the electronic g-tensor are extremely sensitive to the first proton transfer from the phenoxyl oxygen to the imidazole nitrogen (EPT product), leading to a significant increase of the g_X-value of up to 0.003, but are not sensitive to the second proton transfer (E2PT product). In the latter case the change of the g_X-value is much smaller (ca. 0.0001), which is too small to be distinguished even by high frequency EPR. The ¹⁴N hyperfine values are also too similar to allow differentiation between the different protonation states in EPT and E2PT. The magnetic resonance parameters were also calculated as a function of the rotation angles around single bonds. It was demonstrated that rotation of the phenoxyl group results in large positive changes (>0.001) in the g_X-values. Analysis of the data reveals that the main source of these changes is related to the strength of the H-bond between phenoxyl oxygen and the proton(s) on N₁ and N₂ positions of the imidazole.

Toward a Molecular Reorganization Energy-Based Analysis of Third-Order Nonlinear Optical Properties of Polymethine Dyes and J-Aggregates

This work demonstrates the feasibility and applicability of the theory of extended multiphonon electron transitions for the description of nonlinear optical properties of polymethine dyes using quantum chemistry and model calculations. The transformation of a strong one-photon absorption band in dye monomers to a weak two-photon absorption band is rationalized from the electron-nuclear resonance condition. The power law fitting of the results of quantum chemical computations of nonlinear optical properties allows the predicting of the shift of the corresponding Egorov-like resonance curve to the shortest dye in the vinylogous series of dye monomers. The results presented provide an insight and guide for the rational molecular design and application of polymethine dyes.

Electronic g-tensors of nanodiamonds: Dependence on the size, shape, and surface functionalization

The electronic g-tensor dependence on the size, shape, and surface functionalization of nanodiamonds (NDs) is theoretically investigated by selecting dangling bonds and single substitutional nitrogen atoms as a main source of the unpaired electrons. The performed g-tensor calculations reveal that aforementioned paramagnetic impurities introduced into octahedrally shaped ND of C₈₄H₆₄ size behave in a very similar manner as those embedded into a smaller octahedral model of C₃₅H₃₆ size. Since cubic and tetrahedral NDs-C₅₄H₄₈ and C₅₁H₅₂-demonstrate a wider range of g-shift values than octahedral systems, the g-tensor dependence on different shapes can be considered as more pronounced. However, a different surface functionalization scheme, namely, fluorination, results in a much larger variation of the g-shifts, pointing to a significant impact the F atoms have on the local environment of the unpaired electrons in C₃₅F₃₆. A partial surface functionalization of C₃₅H₃₆ with benzoic acid and aniline groups indicates that, in some special cases, these linkers might induce a noticeable spin density redistribution which in turn substantially modifies the g-shift values of the system. Additional infrared (IR) spectra calculations show that some of paramagnetic defects in C₃₅H₃₆ and C₃₅F₃₆ possess clearly expressed signatures which could be useful while analyzing the experimental IR spectra of NDs.

On the magnetic properties of nanodiamonds: Electronic g-tensor calculations

The electronic g-tensor calculations are carried out for various paramagnetic defects introduced into hydrogenated diamond nanocrystal C₃₅H₃₆, showing that such a system can be successfully used to model magnetic properties of nanodiamonds (NDs) with paramagnetic centers containing no vacancies. In addition, it is revealed that, depending on the geometric positions in ND, paramagnetic centers of the same type produce noticeable variations of the g-tensor values. A side-by-side comparison of the performance of effective nuclear charge and spin-orbit mean field (SOMF) approaches indicates that the latter is more sensitive to the quality of basis sets, especially concerning diffuse functions, the inclusion of which is found to be nonbeneficial. What is more, the SOMF method also exhibits a much more pronounced gauge-origin dependence. Compared to electronic charge centroid, spin centers (SCs) demonstrate a superior suitability as gauge origins, providing a better agreement with diamagnetic and paramagnetic contributions of g-tensor obtained employing gauge-including atomic orbitals (GIAOs). Therefore, SCs can be recommended for the g-tensor calculations of NDs whenever GIAOs are not available.

Singlet-triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory

Molecular magnets, defined here as organic polyradicals, can be used as building blocks in the fabrication of novel and structurally diverse magnetic light-weight materials. We present a theoretical investigation of the lowest spin states of several binuclear copper diradicals. In contrast to previous studies, we consider not only the energetics of the low-lying states (which are related to the exchange-coupling parameter within the Heisenberg-Dirac-van-Vleck model), but also the character of the diradical states themselves. We use natural orbitals, their occupations, and the number of effectively unpaired electrons to quantify bonding patterns in these systems. We compare the performance of spin-flip time-dependent density functional theory (SF-TDDFT) using various functionals and effective core potentials against the wave function based approach, equation-of-motion spin-flip coupled-cluster method with single and double substitutions (EOM-SF-CCSD). We find that SF-TDDFT paired with the PBE50 and B5050LYP functionals performs comparably to EOM-SF-CCSD, with respect to both singlet-triplet gaps and states' characters. Visualization of frontier natural orbitals shows that the unpaired electrons are localized on copper centers, in some cases exhibiting slight through-bond interaction via copper d-orbitals and p-orbitals of neighboring ligand atoms. The analysis reveals considerable interactions between the formally unpaired electrons in the antiferromagnetic diradicaloids, meaning that they are poorly described by the Heisenberg-Dirac-van-Vleck model. Thus, for these systems the experimentally derived exchange-coupling parameters are not directly comparable with the singlet-triplet gaps. This explains systematic discrepancies between the computed singlet-triplet energy gaps and the exchange-coupling parameters extracted from experiment.

In silico spectroscopy of tryptophan and tyrosine radicals involved in the long-range electron transfer of cytochrome c peroxidase

Cytochrome c peroxidase (CcP) is a heme-containing enzyme that catalyzes the oxidation of the ferrocytochrome c to ferricytochrome c with concomitant reduction of H2O2 to H2O. Its catalytic cycle involves the formation of a double oxidized species (compound I) consisting of an oxoferryl center (Fe(IV)═O) and an amino acid radical (R(•)). Here we use a quantum-mechanics/molecular-mechanics (QM/MM) computational protocol based on density functional theory (DFT) and multiconfigurational perturbation theory (CASPT2) methods to reproduce specific features of compound I EPR and UV-vis spectra. The results show that the employed QM/MM models can correctly predict the magnetic, electronic and vibrational properties of the observed amino acid radicals of compound I. Furthermore, we have been able to confirm that the principal radical species of compound I is a tryptophan cationic radical located on residue 191 (Trp191(•+)) and that three tyrosine residues (Tyr203, Tyr236, and Tyr251), located along two possible ET pathways involving Trp191(•+), are possible candidates to host the secondary radical species.

The world as viewed by and with unpaired electrons

Recent advances in electron paramagnetic resonance (EPR) include capabilities for applications to areas as diverse as archeology, beer shelf life, biological structure, dosimetry, in vivo imaging, molecular magnets, and quantum computing. Enabling technologies include multifrequency continuous wave, pulsed, and rapid scan EPR. Interpretation is enhanced by increasingly powerful computational models.

Investigating magnetostructural correlations in the pseudooctahedral trans-[Ni(II){(OPPh2)(EPPh2)N}2(sol)2] complexes (E = S, Se; sol = DMF, THF) by magnetometry, HFEPR, and ab initio quantum chemistry

In this work, magnetometry and high-frequency and -field electron paramagnetic resonance spectroscopy (HFEPR) have been employed in order to determine the spin Hamiltonian (SH) parameters of the non-Kramers, S = 1, pseudooctahedral trans-[Ni(II){(OPPh(2))(EPPh(2))N}(2)(sol)(2)] (E = S, Se; sol = DMF, THF) complexes. X-ray crystallographic studies on these compounds revealed a highly anisotropic NiO(4)E(2) coordination environment, as well as subtle structural differences, owing to the nature of the Ni(II)-coordinated solvent molecule or ligand E atoms. The effects of these structural characteristics on the magnetic properties of the complexes were investigated. The accurately HFEPR-determined SH zero-field-splitting (zfs) D and E parameters, along with the structural data, provided the basis for a systematic density functional theory (DFT) and multiconfigurational ab initio computational analysis, aimed at further elucidating the electronic structure of the complexes. DFT methods yielded only qualitatively useful data. However, already entry level ab initio methods yielded good results for the investigated magnetic properties, provided that the property calculations are taken beyond a second-order treatment of the spin-orbit coupling (SOC) interaction. This was achieved by quasi-degenerate perturbation theory, in conjunction with state-averaged complete active space self-consistent-field calculations. The accuracy in the calculated D parameters improves upon recovering dynamic correlation with multiconfigurational ab initio methods, such as the second-order N-electron valence perturbation theory NEVPT2, the difference dedicated configuration interaction, and the spectroscopy-oriented configuration interaction. The calculations showed that the magnitude of D (∼3-7 cm(-1)) in these complexes is mainly dominated by multiple SOC contributions, the origin of which was analyzed in detail. In addition, the observed largely rhombic regime (E/D = 0.16-0.33) is attributed to the highly distorted metal coordination sphere. Of special importance is the insight by this work on the zfs effects of Se coordination to Ni(II). Overall, a combined experimental and theoretical methodology is provided, as a means to probe the electronic structure of octahedral Ni(II) complexes.

Spin interaction in octahedral zinc complexes of mono- and diradical Schiff and mannich bases

The four Schiff bases 2-tert-butyl-4-methoxy-6-[(pyridin-2-ylmethylimino)methyl]phenol, 2,4-di-tert-butyl-6-[(pyridin-2-ylmethylimino)methyl]phenol, 2-tert-butyl-4-methoxy-6-(quinolin-8-yliminomethyl)phenol, and 2,4-di-tert-butyl-6-(quinolin-8-yliminomethyl)phenol) as well as one Mannich base, N,N',N,N'-bis[(2-hydroxy-3,5-di-tert-butylbenzyl)(2-pyridylmethyl)]ethylenediamine, and their zinc bis-phenolate complexes 1-5, respectively, have been prepared. The complexes 4 and 5 have been characterized by X-ray diffraction crystallography, showing a zinc ion within an octahedral environment, with a cis orientation of the phenolate moieties. 1-5 exhibit in their cyclic voltammetry curves two anodic reversible waves attributable to the successive oxidation of the phenolates into phenoxyl radicals. Bulk electrolysis at ca. +0.1 V affords the zinc-coordinated monophenoxyl radical species (1(*))(+)-(5(*))(+) characterized by UV-vis absorption bands at 400-440 nm. The more stable radicals are (3(*))(+) and (4(*))(+) (half-life higher than 90 min at 298 K), likely due to the increased charge delocalization within the quinoline moieties. These species exhibit a significant additional near-IR band (epsilon > 1650 M(-1) cm(-1)) attributed to a CT transition. In the two-electron-oxidized species (1(**))(2+)-(5(**))(2+) the radical spins present a weak magnetic coupling. EPR reveals an antiferromagnetic exchange interaction for (1(**))(2+)-(4(**))(2+), whereas an unusual ferromagnetic exchange coupling is operative in (5(**))(2+). The weak magnitude of experimental |J| values (within the 1-5 cm(-1) range) as well as their sign could be well reproduced by DFT calculations at the B3LYP level. The small energy gap between the ground and the first excited spin states allows us to investigate the zero-field splitting (ZFS) of the triplet by EPR spectroscopy. This parameter is found to be axial for all systems, with |D| values of 0.0163 cm(-1) for (1(**))(2+), 0.0182 cm(-1) for (2(**))(2+), 0.0144 cm(-1) for (3(**))(2+), 0.0160 cm(-1) for (4(**))(2+), and 0.0115 cm(-1) for (5(**))(2+). The trend between experimental ZFS is confirmed by DFT calculations, which give further insight regarding its sign (negative for all the compounds). Lower ZFS values are obtained for (2(**))(2+) compared to (1(**))(2+) (and also for (4(**))(2+) compared to (3(**))(2+)), which can be interpreted by an increased delocalization of the spin density over the methoxy para substituent. Significant spin population on the quinoline also contributes to a lowering of the |D| value, as observed when (3(**))(2+) is compared to (1(**))(2+) (and also when (4(**))(2+) is compared to (2(**))(2+)).

Density functional theory

Density functional theory (DFT) finds increasing use in applications related to biological systems. Advancements in methodology and implementations have reached a point where predicted properties of reasonable to high quality can be obtained. Thus, DFT studies can complement experimental investigations, or even venture with some confidence into experimentally unexplored territory. In the present contribution, we provide an overview of the properties that can be calculated with DFT, such as geometries, energies, reaction mechanisms, and spectroscopic properties. A wide range of spectroscopic parameters is nowadays accessible with DFT, including quantities related to infrared and optical spectra, X-ray absorption and Mössbauer, as well as all of the magnetic properties connected with electron paramagnetic resonance spectroscopy except relaxation times. We highlight each of these fields of application with selected examples from the recent literature and comment on the capabilities and limitations of current methods.

A new quantum chemical approach to the magnetic properties of oligonuclear transition-metal complexes: application to a model for the tetranuclear manganese cluster of photosystem II

The reliable correlation of structural features and magnetic or spectroscopic properties of oligonuclear transition-metal complexes is a critical requirement both for research into innovative magnetic materials and for elucidating the structure and function of many metalloenzymes. We have developed a novel method that for the first time enables the extraction of hyperfine coupling constants (HFCs) from broken-symmetry density functional theory (BS-DFT) calculations on clusters. Using the geometry-optimized tetranuclear manganese complex [Mn(4)O(6)(bpy)(6)](4+/3+) as a model, we first examine in detail the calculation of exchange coupling constants J through the BS-DFT approach. Complications arising from the indeterminacy of experimentally fitted J constants are identified and analyzed. It is found that only the energy levels derived from Hamiltonian diagonalization are a physically meaningful basis for comparing theory and experiment. Subsequently, the proposed theoretical scheme is applied to the calculation of (55)Mn HFCs of the Mn(III,IV,IV,IV) state of the complex, which is similar to the S(2) state of the oxygen-evolving complex (OEC) in photosystem II of oxygenic photosynthesis. The new approach performs reliably and accurately, and yields calculated HFCs that can be directly compared with experimental data. Finally, we carefully examine the dependence of HFC on the J value and draw attention to the sensitivity of the calculated values to the exchange coupling parameters. The proposed strategy extends naturally to hetero-oligonuclear clusters of arbitrary shape and nuclearity, and hence is of general validity and usefulness in the study of magnetic metal clusters. The successful application of the new approach presented here is a first step in the effort to establish correlations between the available spectroscopic information and the structural features of complex metalloenzymes like OEC.