Prediction of EPR g Tensors in Simple d1 Metal Porphyrins with Density Functional Theory

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

Analyses of sizable ZFS and magnetic tensors of high spin metallocomplexes

The fictitious spin-1/2 Hamiltonian approach is the putative method to analyze the fine-structure/hyperfine ESR spectra of high spin metallocomplexes having sizable zerofield splitting (ZFS), thus giving salient principal g-values far from around g = 2 without explicitly providing their ZFS parameters in most cases. Indeed, the significant departure of the g-values from g = 2 is indicative of the occurrence of their high spin states, but naturally they never agree with true g-values acquired by quantum chemical calculations such as sophisticated DFT or ab initio MO calculations. In this work, we propose facile approaches to determine the magnetic tensors of high spin metallocomplexes having sizable ZFS, instead of performing advanced high-field/high-frequency ESR spectroscopy. We have revisited analytical expressions for the relationship between effective g-values and true principal g-values for high spins. The useful analytical formulas for the g^eff-g^true relationships are given for S's up to 7/2. The genuine Zeeman perturbation formalism gives the exact solutions for S = 3/2, and for higher S's it is much more accurate than the pseudo-Zeeman perturbation approach documented so far (A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Metal Ions, 1970; J. R. Pilbrow, J. Magn. Reson., 1978, 31, 479; F. Trandafir et al., Appl. Magn. Reson., 2007, 31, 553; M. Fittipaldi et al., J. Phys. Chem. B, 2008, 112, 3859), in which the E(S_x² - S_y²) term is putatively treated to the second order. To show the usefulness of the present approach, we exploit Fe^III(Cl)OEP (S = 5/2) (OEP: 2,3,7,8,12,13,17,18-octaethylporphyrin) and Co^IIOEP (S = 3/2) well magnetically diluted in the diamagnetic host crystal lattice of Ni^IIOEP. The advantage of single-crystal ESR spectroscopy lies in the fact that the molecular information on the principal axes of the magnetic tensors is crucial in comparing with reliable theoretical results. In high spin states of metallocomplexes with sizable ZFS in pseudo-octahedral symmetry, their fine-structure ESR transitions for the principal z-axis orientation appear in the lower field far from g = 2 at the X-band, disagreeing with the putative intuitive picture obtained using relevant ESR spectroscopy. A Re^III,IV dinuclear complex in a mixed valence state exemplifies the cases, whose fine-structure/hyperfine ESR spectra of the neat crystals have been analyzed in their principal-axis system. The DFT-based/ab initio MO calculations of the magnetic tensors for all the high spin entities in this work were carried out.

Insights into the oxygen-based ligand of the low pH component of the Cu(2+)-amyloid-β complex

In spite of significant experimental effort dedicated to the study of Cu(2+) binding to the amyloid beta (Aβ) peptide, involved in Alzheimer's disease, the nature of the oxygen-based ligand in the low pH component of the Cu(2+)-Aβ(1-16) complex is still under debate. This study reports density-functional-theory-based calculations that explore the potential energy surface of Cu(2+) complexes including N and O ligands at the N-terminus of the Aβ peptide, with a focus on evaluating the role of Asp1 carboxylate in copper coordination. Model conformers including 3, 6, and 17 amino acids have been used to systematically study several aspects of the Cu(2+)-coordination such as the Asp1 side chain conformation, local peptide backbone geometry, electrostatic and/or hydrogen bond interactions, and number and availability of Cu(2+) ligands. Our results show that the Asp1 peptide carbonyl binds to Cu(2+) only if the coordination number is less than four. In contrast, if four ligands are available, the most stable structures include the Asp1 carboxylate in equatorial position instead of the Asp1 carbonyl group. The two lowest energy Cu(2+)-Aβ(1-17) models involve Asp1 COO(-), the N-terminus, and His6 and His14 as equatorial ligands, with either a carbonyl or a water molecule in the axial position. These models are in good agreement with experimental data reported for component I of the Cu(2+)-Aβ(1-16) complex, including EXAFS- and X-ray-derived Cu(2+)-ligand distances, Cu(2+) EPR parameters, and (14)N and (13)C superhyperfine couplings. Our results suggest that at low pH, Cu(2+)-Aβ species with Asp1 carboxylate equatorial coordination coexist with species coordinating the Asp1 carbonyl. Understanding the bonding mechanism in these species is relevant to gain a deeper insight on the molecular processes involving copper-amyloid-β complexes, such as aggregation and redox activity.

Chemical bonding and aromaticity in metalloporphyrins,

We report here the chemical bonding and aromaticity patterns in metalloporphyrins, which were obtained with density functional theory (DFT) calculations at the OPBE/TZP level. This level of theory was previously shown to be very accurate for determining spin-state splittings [J. Chem. Theory Comput. 2008, 4, 2057] of transition-metal complexes. We considered metalloporphyrins along the first-row transition metals (Sc–Zn) extended with alkaline-earth metals (Mg, Ca) and several second-row transition metals (Ru, Pd, Ag, Cd). An energy decomposition analysis was performed to study the metal–ligand interactions, which showed that almost all complexes are significantly stabilized through (covalent) orbital interactions. The only exception is with calcium as the central metal, which interacts with the porphyrin mainly through electrostatic interactions. Furthermore, we studied aromaticity patterns for these complexes by looking at a number of (structural and electronic) aromaticity descriptors, for both the inner-ring and outer-ring of the porphyrin and of the pyrroles. The inner-ring (N16) aromaticity is shown to be unaffected by metal complexation, while the outer-ring (N20) and the pyrrole (N5) aromaticities are found to increase significantly in the metal coordinated porphyrins.

Ambidentate H-bonding by heme-bound NO: structural and spectral effects of -O versus -N H-bonding

Resonance Raman studies have uncovered puzzling complexities in the structures of NO adducts of heme proteins. Although CO adducts of heme proteins obey well-behaved anti-correlations between Fe-C and C-O stretching frequencies, which reflect changes in backbonding induced by distal H-bonding residues, the corresponding NO data are scattered. This scatter can be traced to distal influences, since protein-free NO-hemes do show well-behaved anti-correlations. Why do distal effects produce irregularities in vFeN/ vNO plots but not in vFeC/vCO plots? We show via density functional theory (DFT) computations on model systems that the response to distal H-bonding differs markedly when the NO acceptor atom is N versus O. Backbonding is augmented by H-bonding to O, but the effect of H-bonding to N is to weaken both N-O and N-Fe bonds. The resulting downward deviation from the vFeN/vNO backbonding line increases with increasing H-bond strength. This effect explains the deviations observed for a series of myoglobin variants, in which the strength of distal H-bonding is modulated by distal pocket residue substitutions. Most of the data follow a positive vFeN/vNO correlation with the same slope as that calculated for H-bonding to N. Such deviations are not observed for CO adducts, because the CO pi* orbital is unoccupied, and serves as a delocalized acceptor of H-bonds. H-bonding to N primes NO-heme for reduction to the HNO adduct, a putative intermediate in NO-reducing enzymes.

Computational studies of EPR parameters for paramagnetic molybdenum complexes. II. Larger MoV systems relevant to molybdenum enzymes

The careful validation of modern density functional methods for the computation of electron paramagnetic resonance (EPR) parameters in molybdenum complexes has been extended to a number of low-symmetry MoV systems that model molybdoenzyme active sites. Both g and hyperfine tensors tend to be reproduced best by hybrid density functionals with about 30-40% exact-exchange admixture, with no particular spin contamination problems encountered. Spin-orbit corrections to hyperfine tensors are mandatory for quantitative and, in some cases, even for qualitative agreement. The g11 (g||) component of the g tensor tends to come out too positive when spin-orbit coupling is included only to leading order in perturbation theory. Compared to single-crystal experiments, the calculations reproduce both g- and hyperfine-tensor orientations well, both relative to each other and to the molecular framework. This is significant, as simulations of the EPR spectra of natural-abundance frozen-solution samples frequently do not allow a reliable determination of the hyperfine tensors. These may now be extracted based on the quantum-chemically calculated parameters. In a number of cases, revised simulations of the experimental spectra have brought theory and experiment into substantially improved agreement. Systems with two terminal oxo ligands, and to some extent with an oxo and a sulfido ligand, have been confirmed to exhibit particularly large negative Deltag33 shifts and thus large g anisotropies. This is discussed in the context of the experimental data for xanthine oxidase.

Calculation of EPR g Tensors for Transition-Metal Complexes Based on Multiconfigurational Perturbation Theory (CASPT2)

The computation of the electronic g tensor by two multireference methods is presented and applied to a selection of molecules including CN, BO, AlO, GaO, InO, ZnH, ZnF, O(2), H(2)O(+), O(3) (-), and H(2)CO(+) (group A) as well as TiF(3), CuCl(4) (2-), Cu(NH(3))(4) (2+), and a series of d(1)-MOX(4) (n-) compounds, with M=V, Cr, Mo, Tc, W, Re and X=F, Cl, Br (group B). Two approaches are considered, namely, one in which spin-orbit coupling and the Zeeman effect are included using second-order perturbation theory and another one in which the Zeeman effect is added through first-order degenerate perturbation theory within the ground-state Kramers doublet. The two methods have been implemented into the MOLCAS quantum chemistry software package. The results obtained for the molecules in group A are in good agreement with experiment and with previously reported calculated g values. The results for the molecules in group B vary. While the g values for the d(1) systems are superior to previous theoretical results, those obtained for the d(9) systems are too large compared to the experimental values.

Computational Studies of Electron Paramagnetic Resonance Parameters for Paramagnetic Molybdenum Complexes. 1. Method Validation on Small and Medium-Sized Systems

A variety of density functional methods have been evaluated in the computation of electronic g-tensors and molybdenum hyperfine couplings for systems ranging from the Mo atom through MoIIIN, [MoVOCl4]-, and [MoVOF5]2- to two larger MoV complexes MoXLCl2 (X=O, S; L=tris(3,5-dimethylpyrazolyl)hydroborate anion). In particular, the influence of the molybdenum basis set and of various exchange-correlation functionals with variable admixtures of Hartree-Fock exchange on the computed EPR parameters have been evaluated in detail. Careful basis-set studies have provided a moderate-sized 12s6p5d all-electron basis on molybdenum that gives hyperfine tensors in excellent agreement with much larger basis sets and that will be useful for calculations on larger systems. The best agreement with experimental data for both hyperfine and g-tensors is obtained with hybrid functionals containing approximately 30-40% Hartree-Fock exchange. Only for MoSLCl2 does increasing spin contamination with increasing exact-exchange admixture restrict the achievable computational accuracy. In all cases, spin-orbit corrections to the hyperfine tensors are sizable and have to be included in accurate calculations. Scalar relativistic effects enhance the isotropic Mo hyperfine coupling by approximately 15-20%. Two-component g-tensor calculations with variational inclusion of spin-orbit coupling show that the Deltag parallel components in [MoVOCl4]- and [MoVOF5]2- depend on higher-order spin-orbit contributions and are thus described insufficiently by the usual second-order perturbation approaches. Computed orientations of g- and hyperfine tensors relative to each other and to the molecular framework for the MoXLCl2 complexes provide good agreement between theory and single-crystal electron paramagnetic resonance experiments. In these cases, the hyperfine tensor orientations are influenced only slightly by spin-orbit effects.

Redox Non-innocence of Thioether Macrocycles: Elucidation of the Electronic Structures of Mononuclear Complexes of Gold(II) and Silver(II)

The mononuclear +2 oxidation state metal complexes [Au([9]aneS(3))(2)](2+) and [Ag([18]aneS(6))](2+) have been synthesized and characterized crystallographically. The crystal structure of the Au(II) species [Au([9]aneS(3))(2)](BF(4))(2) shows a Jahn-Teller tetragonally distorted geometry with Au-S(1) = 2.839(5), Au-S(2) = 2.462(5), and Au-S(3) = 2.452(5) A. The related Ag(II) complex [Ag([18]aneS(6))](ClO(4))(2) has been structurally characterized at both 150 and 30 K and is the first structurally characterized complex of Ag(II) with homoleptic thioether S-coordination. The single-crystal X-ray structure of [Ag([18]aneS(6))](ClO(4))(2) confirms octahedral homoleptic S(6)-thioether coordination. At 150 K, the structure contains two independent Ag(II)-S distances of 2.569(7) and 2.720(6) A. At 30 K, the structure retains two independent Ag(II)-S distances of 2.615(6) and 2.620(6) A, with the complex cation retaining 3-fold symmetry. The electronic structures of [Au([9]aneS(3))(2)](2+) and [Ag([18]aneS(6))](2+) have been probed in depth using multifrequency EPR spectroscopy coupled with DFT calculations. For [Au([9]aneS(3))(2)](2+), the spectra are complex due to large quadrupole coupling to (197)Au. Simulation of the multifrequency spectra gives the principal g values, hyperfine (A) and quadrupole (P) couplings, and furthermore reveals non-co-incidence of the principal axes of the P tensor with respect to the A and g matrices. These results are rationalized in terms of the electronic and geometric structure and reveal that the SOMO has ca. 30% Au 5d(xy)() character, consistent with DFT calculations (27% Au character). For [Ag([18]aneS(6))](2+), detailed EPR spectroscopic analysis confirms that the SOMO has ca. 26% Ag 4d(xy)() character and DFT calculations are consistent with this result (22% Ag character).

Where Is the Spin? Understanding Electronic Structure and g-Tensors for Ruthenium Complexes with Redox-Active Quinonoid Ligands

Understanding the bonding in transition metal complexes with redox-active ligands is a major challenge, for example in redox catalysis or in bioinorganic chemistry. In this work, electronic g-tensors, spin-density distributions, and electronic structure have been studied by different density functional methods for an extended series of complexes [Ru(acac)2(L)]n (n = -1, 0, +1; L = redox-active o-quinonoid ligand). Comparison is made with experimental g-tensors and g-tensor-based oxidation-state assignments for a number of experimentally studied examples, using both gradient-corrected (BP86) and hybrid functionals (B3LYP, BHLYP) representing a range of exact-exchange admixtures. Reasonable, albeit not perfect, agreement with experimental g-tensors is obtained in one-component DFT calculations with hybrid functionals. Analyses of spin densities confirm the assignment of the cationic complexes as predominantly d5-Ru(III) with a neutral quinonoid ligand. However, this conclusion is obtained only after inclusion of the appreciable spin polarization of the unrestricted determinant, while the singly occupied molecular orbital (SOMO) is localized more on the acac ligands. The anionic complexes turn out to be approximately halfway between a d6-Ru(II)/semiquinone and a d5-Ru(III)/catecholate formulation, but again only after taking into account the extensive spin polarization. Even the previous assignment of the neutral parent systems as d5-Ru(III)/semiquinone is not accurate, as a d6-Ru(II)/quinone resonance structure contributes to some extent. Very unusual trends in the spin contamination of the Kohn-Sham determinant with increasing exact-exchange admixture in some of the cationic complexes have been traced to an interplay between spin delocalization and spin polarization.

Comparative Density-Functional Study of the Electron Paramagnetic Resonance Parameters of Amavadin

Electronic g tensors and hyperfine coupling tensors have been calculated for amavadin, an unusual eight-coordinate vanadium(IV) complex isolated from Amanita muscaria mushrooms. Different density-functional methods have been compared, ranging from local via gradient-corrected to hybrid functionals with a variable Hartree-Fock exchange admixture. For both electron paramagnetic resonance (EPR) properties, hybrid functionals with an appreciable exact-exchange admixture provide the closest agreement with experimental data. Second-order spin-orbit corrections provide non-negligible contributions to the 51V hyperfine tensor. The orientation of g and A tensors relative to each other also depends on spin-orbit corrections to the A tensor. A rationalization for the close resemblance of the EPR parameters of amavadin to those of the structurally rather different vanadyl complexes is provided, based on the nature of the relevant frontier orbitals.

Determination of the g-Tensors and Their Orientations for cis,trans-(L-N2S2)MoVOX (X = Cl, SCH2Ph) by Single-Crystal EPR Spectroscopy and Molecular Orbital Calculations

A single-crystal study of cis,trans-(L-N2S2)MoVOCl (1) doped into cis,trans-(N2S2)MoVIO2 (3) has enabled the g-tensor of 1 and its orientation with respect to the molecular structure to be determined. The EPR parameters (g1, 2.004; g2, 1.960; g3, 1.946; A1, 71.7 x 10(-4) cm(-1); A2, 11.7 x 10(-4) cm(-1); A3, 32.0 x 10(-4) cm(-1)) of cis,trans-(L-N2S2)MoVOCl [L-N2S2H2 = N,N'-dimethyl-N,N'-bis(mercaptophenyl)ethylenediamine] mimic those of the low-pH form of sulfite oxidase and the "very rapid" species of xanthine oxidase. The principal axis that corresponds to g1 is rotated approximately 10 degrees from the Mo[triple bond]O vector, while the principal axis that corresponds to g3 is located in the equatorial plane and approximately 38 degrees from the Mo-Cl vector. Independent theoretical calculations of the g-tensor of 1 were performed using two types of techniques: (1) the spectroscopically parametrized intermediate neglect of differential overlap technique (INDO/S) combined with single-excitation configuration interaction (CIS); (2) a scalar relativistic DFT (BP86 and B3LYP functionals) treatment using the zeroth order regular approximation to relativistic effects (ZORA) in combination with recently developed accurate multicenter mean field spin-orbit operators (RI-SOMF) and the estimation of solvent effects using dielectric continuum theory at the conductor-like screening model (COSMO) level. The excellent agreement between experiment and theory, as well as the high consistency between the INDO/S and BP86/ZORA results, provides a sound basis for analysis of the calculated orientation of the g-tensor for cis,trans-(L-N2S2)MoVO(SCH2Ph) (2), for which single-crystal EPR data are not available but which contains three equatorial sulfur donor atoms, as occurs in sulfite oxidase and xanthine oxidase. The implications of these results for the EPR spectra of the Mo(V) centers of enzymes are discussed.

Paramagnetic species on catalytic surfaces--DFT investigations into structure sensitivity of the hyperfine coupling constants

Structure sensitivity of the hyperfine coupling constants was investigated by means of DFT calculations for selected surface paramagnetic species. A *CH2OH radical trapped on silica and intrazeolite copper nitrosyl adducts encaged in ZSM-5 were taken as the examples. The surface of amorphous silica was modeled with a [Si5O8H10] cluster, whereas the zeolite hosting sites were epitomized by [Si4AlO5(OH)10]- cluster. Three different coordination modes of the *CH2OH radical were considered and the isotropic 13C and 1H hyperfine constants of the resultant van der Waals complexes, calculated with B3LYP/6-311G(d), were discussed in terms of the angular deformations caused by hydrogen bonds with the cluster. The magnetic parameters of the eta1-N[CuNO]11 and eta1-O[CuNO]11 linkage isomers were calculated at the BPW91/LanL2DZ and 6-311G(df) level. For the most stable eta1-N adduct a clear dependence of the spin density distribution within the Cu-NO moiety on changes in the Cu-N-O angle and the Cu-N bond distance was observed and accounted for by varying spin polarization and delocalization contributions.

Quantitative vibrational dynamics of iron in nitrosyl porphyrins

We use quantitative experimental and theoretical approaches to characterize the vibrational dynamics of the Fe atom in porphyrins designed to model heme protein active sites. Nuclear resonance vibrational spectroscopy (NRVS) yields frequencies, amplitudes, and directions for 57Fe vibrations in a series of ferrous nitrosyl porphyrins, which provide a benchmark for evaluation of quantum chemical vibrational calculations. Detailed normal mode predictions result from DFT calculations on ferrous nitrosyl tetraphenylporphyrin Fe(TPP)(NO), its cation [Fe(TPP)(NO)]+, and ferrous nitrosyl porphine Fe(P)(NO). Differing functionals lead to significant variability in the predicted Fe-NO bond length and frequency for Fe(TPP)(NO). Otherwise, quantitative comparison of calculated and measured Fe dynamics on an absolute scale reveals good overall agreement, suggesting that DFT calculations provide a reliable guide to the character of observed Fe vibrational modes. These include a series of modes involving Fe motion in the plane of the porphyrin, which are rarely identified using infrared and Raman spectroscopies. The NO binding geometry breaks the four-fold symmetry of the Fe environment, and the resulting frequency splittings of the in-plane modes predicted for Fe(TPP)(NO) agree with observations. In contrast to expectations of a simple three-body model, mode energy remains localized on the FeNO fragment for only two modes, an N-O stretch and a mode with mixed Fe-NO stretch and FeNO bend character. Bending of the FeNO unit also contributes to several of the in-plane modes, but no primary FeNO bending mode is identified for Fe(TPP)(NO). Vibrations associated with hindered rotation of the NO and heme doming are predicted at low frequencies, where Fe motion perpendicular to the heme is identified experimentally at 73 and 128 cm-1. Identification of the latter two modes is a crucial first step toward quantifying the reactive energetics of Fe porphyrins and heme proteins.

Density functional calculations on electronic circular dichroism spectra of chiral transition metal complexes

Time-dependent density functional theory (TD-DFT) has for the first time been applied to the computation of circular dichroism (CD) spectra of transition metal complexes, and a detailed comparison with experimental spectra has been made. Absorption spectra are also reported. Various Co(III) complexes as well as [Rh(en)(3)](3+) are studied in this work. The resulting simulated CD spectra are generally in good agreement with experimental spectra after corrections for systematic errors in a few of the lowest excitation energies are applied. This allows for an interpretation and assignment of the spectra for the whole experimentally accessible energy range (UV/vis). Solvent effects on the excitations are estimated via inclusion of a continuum solvent model. This significantly improves the computed excitation energies for charge-transfer bands for complexes of charge +3, but has only a small effect on those for neutral or singly charged complexes. The energies of the weak d-to-d transitions of the Co complexes are systematically overestimated due to deficiencies of the density functionals. These errors are much smaller for the 4d metal complex. Taking these systematic errors and the effect of a solvent into consideration, TD-DFT computations are demonstrated to be a reliable tool in order to assist with the assignment and interpretation of CD spectra of chiral transition metal complexes.

Quantum chemical calculations of spectroscopic properties of metalloproteins and model compounds: EPR and Mössbauer properties

Recently developed theoretical methods to predict EPR and Mössbauer parameters open the way for close interactions between theorists and experimentalists to elucidate the geometric and electronic structures of metalloenzymes and model complexes and to obtain insight into their reactive properties. Spectral calculations (g-values, hyperfine couplings, zero-field splittings, isomer shifts and quadrupole splittings) are also a means to validate theoretical approaches and therefore complement the prediction of geometries, reaction energies and transition states.

The spin distribution in low-spin iron porphyrins

In many low-spin (S = 1/2) iron porphyrin derivatives, electron spin resonance (ESR) spectra indicate that one of the d(pi) orbitals of iron, either a d(xz) or d(yz), depending on the axial ligands of the porphyrin complex as well as their orientation, is essentially singly occupied; the unpaired electron is almost completely located at the metal. In contrast, nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR) spectroscopy convincingly show that a significant share of the unpaired electron is delocalized. This apparent contradiction is explained by the present density-functional-theory (DFT) calculations performed on a heme a model as well as on bis-imidazole-ligated iron porphyrin without substituents. The calculations show that the integrated spin density at the iron atom is nearly one, in agreement with the ESR measurements. However, significant areas with opposite (beta) spin are found along the Fe-N bond axes, thus evoking a need for additional alpha-spin density to be present in the porphyrin ring, ring substituents, and the axial ligands to keep the net amount of unpaired spin exactly one. The gross spin density, that is, the sum of unpaired alpha and beta spins, amounts to about 1.3 electrons. It seems that the degree to which alpha and beta spin dominate in different regions of the heme structure, as evidenced in these calculations, has not been previously observed.

Density functional calculations for modeling the oxidized states of the active site of nickel-iron hydrogenases. 1. Verification of the method with paramagnetic Ni and Co complexes

ZORA relativistic DFT calculations are presented which aim to reproduce geometric structures and EPR properties of [Ni(mnt)(2)](-) (H(2)mnt = maleonitrildithiol), two other paramagnetic low-spin Ni(III) complexes, and an asymmetric paramagnetic Co(II) complex. The study tests the accuracy of the computational method as a prior step to the modeling of the geometric and electronic structure of the active site of NiFe hydrogenases in its EPR-active oxidized states Ni-A and Ni-B. Systematic deviations from experiment are found for the calculated g-values; relative differences among them are, however, well reproduced. Because no significant improvements have been achieved by using larger basis sets or more sophisticated functionals, g-values may be calculated rather rapidly at the VWN level. This is most important for the modeling of the active site of NiFe hydrogenases because its complexity does not permit calculations at high levels of theory. For [Ni(mnt)(2)](-), excellent agreement between calculated and experimental results is obtained for the (14)N quadrupole coupling, whereas the calculated hyperfine couplings are not always in good agreement with experimental data.

Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators

We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.

Electron spin resonance and electronic structure of vanadyl-porphyrin in heavy crude oils

A study of vanadyl-porphyrin by electron spin resonance (ESR) was carried out looking for answers about the role that the central V=O ion plays when these kinds of molecules are present in heavy crude oils. The eigenvalues of the linear combination of atomic orbitals (LCAO) were obtained from the experimental values of g and parameters (ESR). The contributions to the molecular orbitals that describe the various energy levels of vanadyl ion were also obtained for the porphyrin species. The trends of the degree of covalent character of the metal-ligand bonds and the length of the vanadium-oxygen chemical bond are discussed. It is interesting to note that the Fermi contact term, K(eff), is essentially constant for all samples investigated, and it was found to be independent of the calculated electron delocalization (1 - delta(2)) and shows only little variation among the three different samples of oil. The orbital energies derived from our ESR study qualitatively agree with those predicted from MO theory for synthetic vanadyl-porphyrins.

Structural origin of two paramagnetic species in six-coordinated nitrosoiron(II) porphyrins revealed by density functional theory analysis of the g tensors

Potential energy and electron paramagnetic resonance (EPR) g tensor surfaces of model five- and six-coordinated porphyrins were examined. For both types of complexes, the NO ligand is preferably coordinated end-on, with a Fe-N-O bond angle of approximately 140 degrees. In the free five-coordinated structure, NO undergoes free rotation around the axial Fe-N(NO) bond. This motion is strongly coupled to the saddle-type distortion of the porphyrin ligand. Coordination by the second axial ligand (imidazole) raises the calculated barrier for NO rotation to about 1 kcal/mol, which is further increased by displacements of imidazole from the ideal axial position. The potential energy surface for the dissociation of the weakly coordinated imidazole ligand is exceptionally flat, with variation of the Fe-N(Im) bond length between 2.1 and 2.5 A changing the energy by less than 1 kcal/mol. Experimental orientations of both axial ligands, as well as the Fe-N(Im) bond length, are therefore likely to be determined by the environment of the complex. In contrast to the total energy, calculated EPR g-tensors are sensitive to the orientation of the NO ligand and to the Fe-N(Im) bond length. Contrary to a common assumption, the g tensor component closest to the free-electron value does not coincide with the direction of the Fe-N(NO) bond. From comparison of the calculated and experimental g-tensor components for a range of structures, the rhombic ("type I") EPR signal is assigned to a static structure with NO oriented toward the meso-C atom of the prophyrin ring, and RFe-N(Im) approximately 2.1 A (calcd g1 = 1.95, g2 = 2.00, g3 = 2.04; exptl g1 = 1.96-1.98, g2 = 2.00, g3 = 2.06-2.08). The axial ("type II") EPR signal cannot correspond to any of the static structures studied presently. It is tentatively assigned to a partially dissociated six-coordinated complex (RFe-N(Im) > 2.5 A), with a freely rotating NO ligand (calcd g parallel = 2.00, g perpendicular = 2.03; exptl g parallel = 1.99-2.00, g perpendicular = 2.02-2.03).