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.     

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.     

Calculating the electron paramagnetic resonance parameters of exchange coupled transition metal complexes using broken symmetry density functional theory: application to a MnIII/MnIV model compound

The capability of the density functional broken symmetry approach for the calculation of various EPR parameters of exchange coupled metal clusters is demonstrated by studying the experimentally well-investigated [Mn(III)Mn(IV)(mu-O)(2)(mu-OAc)DTNE](2+) complex. Geometry optimizations of the complex in its broken symmetry and high spin states yielded structures with two distinct manganese sites and geometrical parameters in good agreement with the X-ray structure. Exchange coupling constants were calculated from the energy differences between the high spin and broken symmetry states using the Heisenberg spin Hamiltonian. Very good agreement between theory and experiment was achieved with the B3LYP hybrid functional. The g-tensor calculations were performed employing the coupled perturbed Kohn-Sham equations. A strategy for the computation of g-tensor site values is presented and provides single-site g-tensors that are in good agreement with the expectations for Mn(III) and Mn(IV), respectively. Spin projection gave the g-tensor of the coupled manganese complex in very good agreement with the experimental results. Complete (55)Mn hyperfine tensors, including spin-orbit contributions, were calculated and spin-projected. The source of anisotropy in this system could be traced back to the Mn(III) ion in line with the experimental results. The isotropic manganese hyperfine coupling constants were underestimated by factors between 1.4 and 2.5. It is shown that this deficiency is systematic in character and not anchored in the broken symmetry approach. Nuclear quadrupole splitting of the (55)Mn nuclei is shown to be small in this system. In addition, (14)N and (1)H ligand hyperfine data were calculated and compared well with the experimental results. The quality of the extended point-dipole model was demonstrated in application to (1)H anisotropic hyperfine coupling constants.     

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.     

Understanding the electon paramagnetic resonance parameters of protein-bound glycyl radicals

The number of enzymes that require a glycyl-based radical for their function is growing. Here, we provide systematic quantum-chemical studies of spin-density distributions, electronic g-tensors, and hyperfine couplings of various models of protein-bound glycyl radicals. Similarly to what is found in a companion paper on N-acetylglycyl, the small g-anisotropy for this delocalized, unsymmetrical system presents appreciable challenges to state-of-the-art computational methodology. This pertains to the quality of structure optimization, as well as to the choice of the spin-orbit Hamiltonian and the gauge origin of the magnetic vector potential. Environmental effects due to hydrogen bonding are complicated and depend in a subtle fashion on the different intramolecular hydrogen bonding for different conformations of the radical. Indeed, the conformation has the largest overall effect on the computed g-tensors (less so on the hyperfine tensors). This is discussed in the context of different g-tensors obtained by recent high-field electron paramagnetic resonance (EPR) measurements for three different enzymes. On the basis of results of a parallel calibration study for N-acetylglycyl, it is suggested that the glycyl radical observed for E. coli anaerobic RNR may have a fully extended conformation, which differs from those of the corresponding radicals in pyruvate formate-lyase or benzylsuccinate synthase.     

Assessment of higher-order spin�Corbit effects on electronic g-tensors of d 1 transition-metal complexes by relativistic two- and four-component methods

The electronic g-tensors of a series of V, Cr, Mo, W, Tc, and Re d¹ transition-metal complexes have been studied systematically by density functional theory (DFT) methods. The comparison between one-component second-order perturbation theory calculations with two- and four-component first-order perturbation calculations has allowed an assessment of the importance of higher-order spin-orbit contributions. Using an efficient matrix Dirac?CKohn?CSham implementation with relativistic kinetic balance basis sets, it has been possible for the first time to apply four-component DFT also to g-tensors of larger models for biological vanadium, molybdenum, and tungsten metal sites. Higher-order spin?Corbit effects are generally crucial for an accurate determination of the g-tensors in such complexes, in many cases more important than the choice of non-hybrid or hybrid density functional. A systematic scaling analysis of the spin?Corbit integrals shows that second-order spin?Corbit effects may be of the same size as the leading first-order effects and thus alter the computed g-tensors fundamentally, in particular for the 5d species. In the latter case, even third-order effects may be non-negligible.     

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.     

Determination of the g-tensors and their orientations for cis,trans-(L-N2S2)Mo(V)OX (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.     

Understanding the EPR parameters of glycine-derived radicals: the case of N-acetylglycyl in the N-acetylglycine single-crystal environment

As a step toward an in-depth understanding of the electron paramagnetic resonance parameters of glycyl radicals in proteins, the hyperfine tensors and, particularly, the g-tensor of N-acetylglcyl in the environment of a single crystal of N-acetylglycine have been studied by systematic state-of-the-art quantum chemical calculations on various suitable model systems. The quantitative computation of the g-tensors for such glycyl-derived radicals is a veritable challenge, mainly because of the very small g-anisotropy combined with a nonsymmetrical, delocalized spin-density distribution and several atoms with comparable spin-orbit contributions to the g-tensors. The choice of gauge origin of the magnetic vector potential, and of approximate spin-orbit operators, both turn out to be more critical than found in previous studies of g-tensors for organic radicals. Environmental effects, included by supermolecular hydrogen-bonded models, were found to be moderate, because of a partial compensation between the influences from intramolecular and intermolecular hydrogen bonds. The largest effects on the g-tensor are caused by the conformation of the radical. The density functional theory methods employed systematically overestimate both the Delta gx and Delta gy components of the g-tensor. This is important for parallel investigations on the protein-glycyl radicals. The 1H alpha and 13C alpha hyperfine couplings depend only slightly on the supermolecular model chosen and appear less sensitive probes of detailed structure and environment.     

A solid-state 95Mo NMR and computational investigation of dodecahedral and square antiprismatic octacyanomolybdate(IV) anions: is the point-charge approximation an accurate probe of local symmetry?

Solid-state 95Mo NMR spectroscopy is shown to be an efficient and effective tool for analyzing the diamagnetic octacyanomolybdate(IV) anions, Mo(CN)(8)4-, of approximate dodecahedral, D(2d), and square antiprismatic, D(4d), symmetry. The sensitivity of the Mo magnetic shielding (sigma) and electric field gradient (EFG) tensors to small changes in the local structure of these anions allows the approximate D(2d) and D(4d) Mo(CN)(8)4- anions to be readily distinguished. The use of high applied magnetic fields, 11.75, 17.63 and 21.1 T, amplifies the overall sensitivity of the NMR experiment and enables more accurate characterization of the Mo sigma and EFG tensors. Although the magnitudes of the Mo sigma and EFG interactions are comparable for the D(2d) and D(4d) Mo(CN)(8)4- anions, the relative values and orientations of the principal components of the Mo sigma and EFG tensors give rise to 95Mo NMR line shapes that are significantly different at the fields utilized here. Quantum chemical calculations of the Mo sigma and EFG tensors, using zeroth-order regular approximation density functional theory (ZORA DFT) and restricted Hartree-Fock (RHF) methods, have also been carried out and are in good agreement with experiment. The most significant and surprising result from the DFT and RHF calculations is a significant EFG at Mo for an isolated Mo(CN)(8)4- anion possessing an ideal square antiprismatic structure; this is contrary to the point-charge approximation, PCA, which predicts a zero EFG at Mo for this structure.     

Relativistic two-component calculations of electronic g-tensors that include spin polarization

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative deltag(parallel)-values of heavy-atom 2sigma radicals and the negative deltag(perpendicular) components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

Assignment of the electronic spectra of [Mo(CN)(8)](4)(-) and [W(CN)(8)](4)(-) by Ab initio calculations

CASPT2 calculations are performed on the dodecahedral and square antiprismatic isomers of the [Mo(CN)(8)](4)(-) and [W(CN)(8)](4)(-) complexes. The high-energy experimental bands above 40000 cm(-)(1) are assigned to MLCT transitions. The experimental observed trend of the extinction coefficients for the molybdenum and tungsten complex is reproduced by our CASSCF oscillator strengths. All bands below 40000 cm(-)(1) can be ascribed to ligand-field transitions, although small contributions from forbidden MLCT transitions cannot be excluded. In order to account for all experimental bands in the electronic spectrum of these octacyanocomplexes, a dynamic equilibrium in solution between the two isomeric forms must be hypothesized. Spin-orbit coupling effects are found to be more important for the square antiprismatic isomers; in particular, large singlet-triplet mixings are calculated for this isomer of [W(CN)(8)](4)(-). Ligand-field and Racah parameters as well as spin-orbit coupling constants are determined on the basis of the calculated transition energies. The obtained values for these parameters support the recently proposed model for exchange interactions in magnetic clusters and networks containing pentavalent octocyanometalates of molybdenum and tungsten.     

Second-order polarization propagator calculations of indirect nuclear spin-spin coupling tensors in the water molecule

The contribution to indirect nuclear spin-spin coupling tensors provided by the Fermi contact, the spin-dipolar, the Fermi contact/spin-dipolar crossterm, and the paramagnetic spin-orbit interactions are investigated in a zeroth-, first- (the same as the coupled Hartree-Fock method), and second-order polarization propagator approach. Numerical applications to the water molecule show that the second-order results for both the HO and the HH coupling constants are in good agreement with experimental data - especially if vibrational corrections and the diamagnetic spin-orbit contributions are taken into account. We find that the correlation corrections beyond coupled Hartree-Fock are important. We also report how the second-order results are influenced by neglect of some of the most time-consuming steps in the calculation.     

About the calculation of exchange coupling constants in polynuclear transition metal complexes

The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H. He and CH(2). He units to compare with Hartree-Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data.     

Structure and electron paramagnetic resonance parameters of the manganese site of concanavalin A studied by density functional methods

The EPR parameters of the manganese site in the saccharide-binding protein concanavalin A have been studied by density functional methods, with an emphasis on metal (⁵⁵Mn) and ligand (¹H and ¹⁷O) hyperfine couplings, in comparison with high-field EPR and ENDOR data. Results for gradient-corrected and hybrid functionals with different exact-exchange admixture have been compared with experiment for the ⁵⁵Mn and the ¹H ligand hyperfine coupling and have been predicted for ¹⁷O hyperfine coupling based on comparison with experiment for the related [Mn(H₂O)₆]²⁺. Appreciable exact-exchange admixture in the hybrid functional is needed to obtain an adequate spin-density distribution and thus near-quantitative agreement with experimental EPR parameters. The common use of experimental proton hyperfine coupling tensors together with the point-dipole approximation for determination of bond lengths is evaluated by explicit calculations.     

DFT analysis of g and 13C hyperfine coupling tensors for model Ni(I)(CO)(n)L(m) (n = 1-4, L = H2O, OH-) complexes epitomizing surface nickel(I) carbonyls

Relativistic calculations within the spin-orbit mean-field (SOMF) approximation, the zero-order regular approximation (ZORA), and the scalar relativistic method based on the Pauli Hamiltonian were performed for the prediction and interpretation of the electronic g tensor and (13)C hyperfine tensor for a set of model polycarbonyl nickel(I) complexes with aqua or hydroxy coligands. They exhibit extensive similarities with heterogeneous [Ni(I)(CO)(n)]-surface complexes produced upon adsorption of carbon monoxide on Ni(I) ions grafted on silica or inside the zeolite channels. Benchmark calculations showing the influence of the exchange-correlation functional on the g tensor were carried out for well-defined nickel(I) complexes of known structure. On this basis, the SOMF-B3LYP scheme was chosen for calculations of the g tensor, and the obtained results were in satisfactory agreement with literature EPR data found for the [Ni(I)(CO)(n)]/SiO(2) system. The calculated g and A((13)C) tensors allowed polycarbonyl complexes of various stereochemistries to be distinguished. The nature of the Deltag(ii) shifts was assessed in terms of the molecular orbital contributions due to the magnetic-field-induced couplings and their structure sensitivity. The noncoincidence of g and (13)C hyperfine principal axes and their orientation with respect to the molecular framework was also examined. The ability of DFT calculations to follow consistently variations of the EPR parameters induced by stereochemical changes around the Ni(I) center provides an invaluable reference for the interpretation of experimental results.     

Resolution of identity Dirac-Kohn-Sham method using the large component only: Calculations of g-tensor and hyperfine tensor

A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall's [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations.