Hybrid density functional approach to the structures and EPR parameters of σ-type iminoxy radicals: the case of 3-oxobutan-2-iminoxyl

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants

Electron paramagnetic resonance (EPR) spectroscopy has been proven to be an important technique for studying paramagnetic systems. Probably, the most accessible EPR parameter and the one that provides a significant amount of information about molecular structure and spin density is the hyperfine coupling constant (HFCC). Hence, accurate quantum-chemical modeling of HFCCs is frequently essential to the adequate interpretation of EPR spectra. It requires the precise spin density, which is the difference between the densities of α- and β-electrons, and thus, its quality is expected to reflect the quality of the total electron density. The question of which approximate exchange-correlation density functional yields sufficiently accurate HFCCs, and thus, the spin density remains open. To assess the performance of well-established density functionals for calculating HFCCs, we used a series of 26 small paramagnetic species and compared the obtained results to the CCSD reference values. The performance of DFT was also tested on EPR-studied o-semiquinone radical interacting with water molecules and Mg²⁺ cation. The HFCCs were additionally calculated by the DLPNO-CCSD method, and this wave function-based technique was found superior to all functionals we tested. Although some functionals were found, on average, to be fairly efficient, we found that the most accurate functional is system-dependent, and therefore, the DLPNO-CCSD method should be preferred for theoretical investigations of the HFCCs and spin density.

Toward an Understanding of the Ambiguous Electron Paramagnetic Resonance Spectra of the Iminoxy Radical from o-Fluorobenzaldehyde Oxime: Density Functional Theory and ab Initio Studies

Iminoxy radicals (R1R2C═N—O•) possess an inherent ability to exist as E and Z isomers. Although isotropic hyperfine couplings for the species with R1 = H allow one to distinguish between E and Z, unequivocal assignment of the parameters observed in the EPR spectra of the radicals without the hydrogen atom at the azomethine carbon to the right isomer is not a simple task. The iminoxyl derived from o-fluoroacetophenone oxime (R1 = CH3 and R2 = o-FC6H5) appears to be a case in point. Moreover, for its two isomers the rotation of the o-FC6H5 group brings into existence the syn and anti conformers, depending on the mutual orientation of the F atom and C═N—O• group, making a description of hyperfine couplings to structure even more challenging. To accomplish this, a vast array of theoretical methods (DFT, OO-SCS-MP2, QCISD) was used to calculate the isotropic hyperfine couplings. The comparison between experimental and theoretical values revealed that the E isomer is the dominant radical form, for which a fast interconversion between anti and syn conformers is expected. In addition, the origin of the significant AF increase with solvent polarity was analyzed.

Metallobiliverdin radicals--DFT studies

Several aspects of the molecular and electronic structure of biliverdin derivatives have been studied using density functional theory (DFT). The calculations have been performed for complexes of trianion (BvO2)3- and dianion [BvO(OH)]2-, derived from two tautomeric forms of biliverdin, BvO2H3 and [BvO(OH)]H2, with redox innocent metal ions: lithium(I), zinc(II), and gallium(III). One-electron-oxidized and reduced forms of each complex (cation and anion radicals) have been also considered. The molecular structures of all species investigated are characterized by a helical arrangement of tetrapyrrolic ligands with the metal ion lying in the plane formed by the two central pyrrole rings. The spin density distribution in four types of metallobiliverdin radicals--[(BvO2.)Mn+]n-2,[[BvO(OH).]Mn+]n-1 (cation radicals),[(BvO2.)Mn+]n-4,[[BvO(OH).]Mn+]n-3 (anion radicals)--has been investigated. In general, the absolute values of spin density on meso carbon atoms were larger than for the beta-carbon atoms. Sign alteration of spin density has been found for meso positions, and also for the beta-carbon atoms of at least two pyrrole rings. The calculated spin density maps accounted for the essential NMR spectroscopic features of iron biliverdin derivatives, including the considerable isotropic shifts detected for the meso resonances and shift alteration at the meso and beta-positions.