The hyperfine structures of small radicals from density functional calculations

Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory

We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO⁺, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving S_z symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.

Optimized Basis Sets for Calculation of Electron Paramagnetic Resonance Hyperfine Coupling Constants: aug-cc-pVTZ-J for the 3d Atoms Sc-Zn

The hyperfine coupling tensor of electron paramagnetic resonance (EPR), describing the interaction between an electron and a given nuclei, depends strongly on the electron density at the nucleus. With standard Gaussian-type orbital basis sets (GTOs), employed in most calculations, it is difficult to obtain converged results of the hyperfine coupling tensor, and basis sets with more flexible core regions have therefore been devised. To this class of core property basis sets belong the aug-cc-pVTZ-J basis sets developed for the s- and p-block atoms. Here, we extend the aug-cc-pVTZ-J basis sets to include the 3d elements Sc-Zn. The converged optimal basis sets are throughout the series described by a (25s17p10d3f2g)/[17s10p7d3f2g] contraction scheme, where four tight s-, one tight p-, and one tight d-type function have been added to the original aug-cc-pVTZ basis sets. The basis sets are generally contracted, and molecular orbital coefficients are used as contraction coefficients. By validation studies with different functionals and compounds, it is shown that the values of the contraction coefficient are effectively independent of the compound used in their generation and the exchange-correlation functional employed in the calculation.

Thermodynamics of the hydroxyl radical addition to isoprene

Oxidation of isoprene by the hydroxyl radical leads to tropospheric ozone formation. Consequently, a more complete understanding of this reaction could lead to better models of regional air quality, a better understanding of aerosol formation, and a better understanding of reaction kinetics and dynamics. The most common first step in the oxidation of isoprene is the formation of an adduct, with the hydroxyl radical adding to one of four unsaturated carbon atoms in isoprene. In this paper, we discuss how the initial conformations of isoprene, s-trans and s-gauche, influences the pathways to adduct formation. We explore the formation of pre-reactive complexes at low and high temperatures, which are often invoked to explain the negative temperature dependence of this reaction's kinetics. We show that at higher temperatures the free energy surface indicates that a pre-reactive complex is unlikely, while at low temperatures the complex exists on two reaction pathways. The theoretical results show that at low temperatures all eight pathways possess negative reaction barriers, and reaction energies that range from -36.7 to -23.0 kcal x mol(-1). At temperatures in the lower atmosphere, all eight pathways possess positive reaction barriers that range from 3.8 to 6.0 kcal x mol(-1) and reaction energies that range from -28.8 to -14.4 kcal x mol(-1).

Density functional theory predictions of isotropic hyperfine coupling constants

The reliability of density functional theory (DFT) in the determination of the isotropic hyperfine coupling constants (hfccs) of the ground electronic states of organic and inorganic radicals is examined. Predictions using several DFT methods and 6-31G, TZVP, EPR-III and cc-pVQZ basis sets are made and compared to experimental values. The set of 75 radicals here studied was selected using a wide range of criteria. The systems studied are neutral, cationic, anionic; doublet, triplet, quartet; localized, and conjugated radicals, containing 1H, 9Be, 11B, 13C, 14N, 17O, 19F, 23Na, 25Mg, 27Al, 29Si, 31P, 33S, and 35Cl nuclei. The considered radicals provide 241 theoretical hfcc values, which are compared with 174 available experimental ones. The geometries of the studied systems are obtained by theoretical optimization using the same functional and basis set with which the hfccs were calculated. Regression analysis is used as a basic and appropriate methodology for this kind of comparative study. From this analysis, we conclude that DFT predictions of the hfccs are reliable for B3LYP/TZVP and B3LYP/EPR-III combinations. Both functional/basis set scheme are the more useful theoretical tools for predicting hfccs if compared to other much more expensive methods.

Sulfur radical cation-peptide bond complex in the one-electron oxidation of S-methylglutathione

Neighboring group participation was investigated in the *OH-induced oxidation of S-methylglutathione in aqueous solutions. Nanosecond pulse radiolysis was used to obtain the spectra of the reaction intermediates and their kinetics. Depending on the pH, and the concentration of S-methylglutathione, pulse irradiation leads to different transients. The transients observed were an intramolecularly bonded [>S thereforeNH2]+ intermediate, intermolecularly S thereforeS-bonded radical cation, alpha-(alkylthio)alkyl radicals, alpha-amino-alkyl-type radical, and an intramolecularly (S thereforeO)+-bonded intermediate. The latter radical is of particular note in that it supports recent observations of sulfur radical cations complexed with the oxygen atoms of peptide bonds and thus has biological and medical implications. This (S thereforeO)+-bonded intermediate had an absorption maximum at 390 nm, and we estimated its formation rate to be >or=6x10(7) s(-1). It is in equilibrium with the intermolecularly S thereforeS-bonded radical cation, and they decay together on the time scale of a few hundred microseconds. The S thereforeS-bonded radical cation is formed from the monomeric sulfur radical cation (>S*+) and an unoxidized S-methylglutathione molecule with the rate constant of 1.0x10(9) M(-1) s(-1). The short-lived [>S thereforeNH2]+ intermediate is a precursor of decarboxylation, absorbs at approximately 390 nm, and decays on the time scale of hundreds of nanoseconds. Additional insight into the details of the association of sulfur radical cations with the oxygen atoms of the peptide bonds was gained by comparing the behavior of the S-methylglutathione (S thereforeO+-bonded five-membered ring) with the peptide gamma-Glu-Met-Gly (S thereforeO+-bonded six-membered ring). Conclusions from experimental observations were supported by molecular modeling calculations.

EPR and DFT study on the stabilization of radiation-generated methyl radicals in dehydrated Na-A zeolite

Electron paramagnetic resonance (EPR) spectroscopy was applied to study paramagnetic species stabilized in Na-A zeolite exposed to gaseous methane and gamma-irradiated at 77 K. Two types of EPR spectra were recorded during thermal annealing of zeolite up to room temperature. Owing to the results for the zeolite exposed to (13)CH(4) the multiplet observed at 110 K was assigned to a (.-)CH(3)...Na(+) complex. After decay of the multiplet, the isotropic quartet of methyl radical was recorded in the temperature range of 170-280 K. On the basis of the EPR parameters it is postulated that (.-)CH(3) radicals in this temperature region are able to freely rotate inside the zeolite cage. The structures of the (.-)CH(3)...Na(+) adsorption complex and respective hyperfine coupling constants were calculated by applying DFT quantum chemical methods. Two different models were applied to represent the zeolite framework: the 6T structure of one six-membered ring and the 3T cluster. The hyperfine coupling constants calculated for the (.-)CH(3)...Na(+) adsorption complex for both applied models show very good agreement with those obtained experimentally.

DFT calculations of magnetic parameters for molybdenum complexes and hydroxymethyl intermediates trapped on silica surface

Density functional theory (DFT) calculations of EPR parameters and their structure sensitivity for selected surface paramagnetic species involved in oxidative dehydrogenation of methanol over silica grafted molybdenum catalyst were investigated. Two surface complexes, Mo(4c)/SiO2 and {O(-)-Mo(4c)}/SiO2, as well as *CH2OH radical trapped on the SiO2 matrix were taken as the examples. The spin-restricted zeroth order regular approximation (ZORA) implemented in the Amsterdam Density Functional suite was used to calculate the electronic g tensor for those species. The predicted values were in satisfactory agreement with experimental EPR results. Five different coordination modes of the *CH2OH radical on the silica surface were considered and the isotropic 13C, 17O, and 1H hyperfine coupling constants (HFCC) of the resultant surface complexes were calculated. Structure sensitivity of the HFCC values was discussed in terms of the angular deformations caused by hydrogen bonding with the silica surface.

Density-functional calculations of relativistic spin-orbit effects on nuclear magnetic shielding in paramagnetic molecules

Terms arising from the relativistic spin-orbit effect on both hyperfine and Zeeman interactions are introduced to density-functional theory calculation of nuclear magnetic shielding in paramagnetic molecules. The theory is a generalization of the former nonrelativistic formulation for doublet systems and is consistent to O(alpha4), the fourth power of the fine structure constant, for the spin-orbit terms. The new temperature-dependent terms arise from the deviation of the electronic g tensor from the free-electron g value as well as spin-orbit corrections to hyperfine coupling tensor A, the latter introduced in the present work. In particular, the new contributions include a redefined isotropic pseudocontact contribution that consists of effects due to both the g tensor and spin-orbit corrections to hyperfine coupling. The implementation of the spin-orbit terms makes use of all-electron atomic mean-field operators and/or spin-orbit pseudopotentials. Sample results are given for group-9 metallocenes and a nitroxide radical. The new O(alpha4) corrections are found significant for the metallocene systems while they obtain small values for the nitroxide radical. For the isotropic shifts, none of the three beyond-leading-order hyperfine contributions are negligible.

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.

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.

Theoretical Study of the Trapping of the OOH Radical by Coenzyme Q

The reactivity of the hydroperoxyl radical with coenzyme Q, as a prototypical chemical reaction involved in biological antioxidant actions, was studied theoretically. Two pathways were analyzed: the hydrogen abstraction reaction from the phenolic hydrogen on the reduced form (ubiquinol), and OOH addition on the oxidized form (ubiquinone). Optimized geometries, harmonic vibrational frequencies, and energies of the stationary points (reactants, intermediate complexes, transition states, and products) for each pathway were calculated at the BHandHLYP/6-31G level of theory. The reaction paths for the two mechanisms were traced independently, and the respective thermal rate constants were calculated using variational transition-state theory with multidimensional small-curvature tunneling. We found that the reactivity of the OOH radical is dominated by the hydrogen abstraction mechanism on ubiquinol, with a rate constant of 5.32 x 10(5) M(-1) s(-1), at 298 K. This result strongly contrasts with that, also obtained by our group, for the more reactive OH radical, which attacks ubiquinone by an addition mechanism, with a diffusion-controlled rate of 6.25 x 10(10) M(-1) s(-1), at 298 K.

Nuclear magnetic resonance shifts in paramagnetic metalloporphyrins and metalloproteins

We report the first detailed investigation of the (1)H, (13)C, (15)N, and (19)F nuclear magnetic resonance (NMR) spectroscopic shifts in paramagnetic metalloprotein and metalloporphyrin systems. The >3500 ppm range in experimentally observed hyperfine shifts can be well predicted by using density functional theory (DFT) methods. Using spin-unrestricted methods together with large, locally dense basis sets, we obtain very good correlations between experimental and theoretical results: R(2) = 0.941 (N = 37, p < 0.0001) when using the pure BPW91 functional and R(2) = 0.981 (N = 37, p < 0.0001) when using the hybrid functional, B3LYP. The correlations are even better for C(alpha) and C(beta) shifts alone: C(alpha), R(2) = 0.996 (N = 8, p < 0.0001, B3LYP); C(beta), R(2) = 0.995 (N = 8, p < 0.0001, B3LYP), but are worse for C(meso), in part because of the small range in C(meso) shifts. The results of these theoretical calculations also lead to a revision of previous heme and proximal histidine residue (13)C NMR assignments in deoxymyoglobin which are confirmed by new quantitative NMR measurements. Molecular orbital (MO) analyses of the resulting wave functions provide a graphical representation of the spin density distribution in the [Fe(TPP)(CN)(2)](-) (TPP = 5,10,15,20-tetraphenylporphyrinato) system (S = (1)/(2)), where the spin density is shown to be localized primarily in the d(xz) (or d(yz)) orbital, together with an analysis of the frontier MOs in Fe(TPP)Cl (S = (5)/(2)), Mn(TPP)Cl (S = 2), and a deoxymyoglobin model (S = 2). The ability to now begin to predict essentially all heavy atom NMR hyperfine shifts in paramagnetic metalloporphyrins and metalloproteins using quantum chemical methods should open up new areas of research aimed at structure prediction and refinement in paramagnetic systems in much the same way that DFT methods have been used successfully in the past to predict/refine elements of diamagnetic heme protein structures.

Relativistic spin-orbit coupling effects on secondary isotope shifts of (13)C nuclear shielding in CX(2) (X = O, S, Se, Te)

Rovibrational corrections, temperature dependence, and secondary isotope shifts of the (13)C nuclear shielding in CX(2) (X = O, S, Se, Te) are calculated taking into account the relativistic spin-orbit (SO) interaction. The SO effect is considered for the first time for the secondary isotope shifts. The nuclear shielding hypersurface in terms of nuclear displacements is calculated by using a density-functional theory method. Ab initio multiconfiguration self-consistent field calculations are done at the equilibrium geometry for comparison. (13)C NMR measurements are carried out for CS(2). The calculated results are compared with both present and earlier experimental data on CO(2), CS(2), and CSe(2). The heavy-atom SO effects on the rovibrational corrections of (13)C shielding are shown to be significant. For CSe(2) and CTe(2), reliable prediction of secondary isotope effects and their temperature dependence requires the inclusion of the SO corrections. In particular, earlier discrepancies of theory and experiment for CSe(2) are fully resolved by taking the SO interactions into account.