Markéta Munzarová

Understanding the electronic factors responsible for ligand spin-orbit NMR shielding in transition-metal complexes

The significant role of relativistic effects in altering the NMR chemical shifts of light nuclei in heavy-element compounds has been recognized for a long time; however, full understanding of this phenomenon in relation to the electronic structure has not been achieved. In this study, the recently observed qualitative differences between the platinum and gold compounds in the magnitude and the sign of spin-orbit-induced (SO) nuclear magnetic shielding at the vicinal light atom ((13)C, (15)N), σ(SO)(LA), are explained by the contractions of 6s and 6p atomic orbitals in Au complexes, originating in the larger Au nuclear charge and stronger scalar relativistic effects in gold complexes. This leads to the chemical activation of metal 6s and 6p atomic orbitals in Au complexes and their larger participation in bonding with the ligand, which modulates the propagation of metal-induced SO effects on the NMR signal of the LA via the Spin-Orbit/Fermi Contact (SO/FC) mechanism. The magnitude of the σ(SO)(LA) in these square-planar complexes can be understood on the basis of a balance between various metal-based 5d → 5d* and 6p → 6p* orbital magnetic couplings. The large and positive σ(SO)(LA) in platinum complexes is dominated by the shielding platinum-based 5d → 5d* magnetic couplings, whereas small or negative σ(SO)(LA) in gold complexes is related to the deshielding contribution of the gold-based 6p → 6p* magnetic couplings. Further, it is demonstrated that σ(SO)(LA) correlates quantitatively with the extent of M-LA electron sharing that is the covalence of the M-LA bond (characterized by the QTAIM delocalization index, DI). The present findings will contribute to further understanding of the origin and propagation of the relativistic effects influencing the experimental NMR parameters in heavy-element systems.

Mechanism of Spin-Orbit Effects on the Ligand NMR Chemical Shift in Transition-Metal Complexes: Linking NMR to EPR

Relativistic effects play an essential role in understanding the nuclear magnetic resonance (NMR) chemical shifts in heavy-atom compounds. Particularly interesting from the chemical point of view are the relativistic effects due to heavy atom (HA) on the NMR chemical shifts of the nearby light atoms (LA), referred to as the HALA effects. The effect of Spin-Orbit (SO) interaction originating from HA on the nuclear magnetic shielding at a neighboring LA, σ(SO), is explored here in detail for a series of d(6) complexes of iridium. Unlike the previous findings, the trends in σ(SO) observed in this study can be fully explained neither in terms of the s-character of the HA-LA bonding nor by trends in the energy differences between occupied and virtual molecular orbitals (MOs). Rather, the σ(SO) contribution to the total NMR shielding is found to be modulated by the d-orbital participation of the heavy atom (Ir) in the occupied and virtual spin-orbit active MOs, i.e., those which contribute significantly to the σ(SO). The correlation between the d-character of σ(SO)-active MOs and the size of the corresponding SO contribution to the nuclear magnetic shielding constant at LA is so tight that the magnitude of σ(SO) can be predicted in a given class of compounds on the basis of d-orbital character of relevant MO with relative error smaller than 15%. This correspondence is supported by an analogy between the perturbation theory expressions for the spin-orbit induced NMR σ-tensor and those for the EPR g-tensor as well as the A-tensor of the ligand. This correlation is demonstrated on a series of d(5) complexes of iridium. Thus, known qualitative relationships between electronic structure and EPR parameters can be newly applied to reproduce, predict, and understand the SO-induced contributions to NMR shielding constants of light atoms in heavy-atom compounds.

Phosphorus Chemical Shifts in a Nucleic Acid Backbone from Combined Molecular Dynamics and Density Functional Calculations

A comprehensive quantum chemical analysis of the influence of backbone torsion angles on (31)P chemical shifts in DNAs has been carried out. An extensive DFT study employed snapshots obtained from the molecular dynamics simulation of [d(CGCGAATTCGCG)]2 to construct geometries of a hydrated dimethyl phosphate, which was used as a model for the phosphodiester linkage. Our calculations provided differences of 2.1 ± 0.3 and 1.6 ± 0.3 ppm between the B(I) and B(II) chemical shifts in two B-DNA residues of interest, which is in a very good agreement with the difference of 1.6 ppm inferred from experimental data. A more negative (31)P chemical shift for a residue in pure BI conformation compared to residues in mixed B(I)/B(II) conformation states is provided by DFT, in agreement with the NMR experiment. Statistical analysis of the MD/DFT data revealed a large dispersion of chemical shifts in both B(I) and B(II) regions of DNA structures. δP ranges within 3.5 ± 0.8 ppm in the B(I) region and within 4.5 ± 1.5 ppm in the B(II) region. While the (31)P chemical shift becomes more negative with increasing α in B(I)-DNA, it has the opposite trend in B(II)-DNA when both α and ζ increase simultaneously. The (31)P chemical shift is dominated by the torsion angles α and ζ, while an implicit treatment of β and ε is sufficient. The presence of an explicit solvent leads to a damping and a 2-3 ppm upfield shift of the torsion angle dependences.

Validation of Relativistic DFT Approaches to the Calculation of NMR Chemical Shifts in Square-Planar Pt2+ and Au3+ Complexes

Recently implemented hybrid density functional methods of calculating nuclear magnetic shielding using the two-component zeroth-order regular approximation approach (J. Phys. Chem. A2009, 113, 11495) have been employed for a series of compounds containing heavy transition-metal atoms. These include Pt(2+), Pd(2+), and Au(3+) organometallics and metal complexes with azines, some of which exhibit interesting biological and catalytic activities. In this study we investigate the effects of geometry, exchange-correlation functional, solvent, and scalar relativistic and spin-orbit corrections on the nuclear magnetic shielding-mainly for (13)C and (15)N atoms connected to a heavy-atom center. Our calculations demonstrate that the B3LYP method using effective core potentials and a cc-pwCVTZ-PP/6-31G** basis set augmented with the polarizable continuum model of the dimethylsulfoxide solvent provides geometries for the complexes in question which are compatible with the experimental NMR results in terms of both the trends and the absolute values of the (13)C shifts. The important role of the exact exchange admixture parameter for hybrid functionals based on B3LYP and PBE0 is investigated systematically for selected Pt(2+) and Au(3+) complexes. The (13)C and (15)N NMR chemical shifts are found to be best reproduced by using a B3LYP or PBE0 approach with 30% and 40-50% exact exchange admixtures for the Pt(2+) and Au(3+) complexes, respectively. The spin-orbit contributions to the (15)N NMR chemical shifts reflect metal-ligand bonding that is much more ionic for the Au(3+) than for the Pt(2+) complex. Finally, an optimized density functional method is applied to a series of transition-metal complexes to estimate the scope and the limitations of the current approach.

Toward Reproducing Sequence Trends in Phosphorus Chemical Shifts for Nucleic Acids by MD/DFT Calculations

This work addresses the question of the ability of the molecular dynamics-density functional theory (MD/DFT) approach to reproduce sequence trend in (31)P chemical shifts (δP) in the backbone of nucleic acids. δP for [d(CGCGAATTCGCG)]2, a canonical B-DNA, have been computed using density functional theory calculations on model compounds with geometries cut out of snapshots of classical molecular dynamics (MD) simulations. The values of (31)P chemical shifts for two distinct B-DNA subfamilies BI and BII, δP/BI and δP/BII, have been determined as averages over the BI and BII subparts of the MD trajectory. This has been done for various samplings of MD trajectory and for two sizes of both the model and the solvent embedding. For all of the combinations of trajectory sampling, model size, and embedding size, sequence dependence of δP/BI in the order of 0.4-0.5 ppm has been obtained. Weighted averages for individual (31)P nuclei in the studied DNA double-helix have been calculated from δP/BI and δP/BII using BI and BII percentages from free MD simulations as well as from approaches employing NMR structural restraints. A good qualitative agreement is found between experimental sequence trends in δP and theoretical δP employing short (24 ns) MD run and BI, BII percentages determined by Hartmann et al. or via MD with the inclusion of NMR structural restraints. Theoretical δP exhibit a systematic offset of ca. 11 ppm and overestimation of trends by a factor of ca. 1.7. When scaled accordingly, theoretical δP/BI and δP/BII can be used to determine the expected percentage of BII to match the experimental value of δP. As evidenced by the calculations on snapshots from Car-Parrinello molecular dynamics, the systematic offsets of the theoretical δP obtained by MD/DFT approach result primarily from the unrealistic bond lengths employed by classical MD. The findings made in this work provide structure-δP relationships for possible use as NMR restraints and suggest that NMR calculations on MD snapshots can be in the future employed for the validation of newly developed force fields.

31P Chemical Shift Tensors for Canonical and Non-canonical Conformations of Nucleic Acids: A DFT Study and NMR Implications

31P chemical shift anisotropy (CSA) tensors have been calculated for a set of selected DNA and RNA backbone conformations using density functional theory. The set includes canonical A-RNA, A-DNA, BI-DNA, BII-DNA, ZI-DNA, and ZII-DNA as well as four A-RNA-type, seven non-A-RNA-type, and three non-canonical DNA conformations. Hexahydrated dimethyl phosphate has been employed as a model. The 31P chemical shift tensors obtained are discussed in terms of similarities in the behavior observed for gauche-gauche (gg) and gauche-trans (gt) conformations around the P-O bonds. We show that torsion angles alpha and zeta are major determinants of the isotropic chemical shift deltaiso and of the deltaCSA11 component of the traceless chemical shift tensor, which is revealed in separate ranges of both deltaiso and deltaCSA11 for gg- and gt-conformers, respectively. A clear distinction between the two conformation types has not been found for the deltaCSA22 and deltaCSA33 components, which is attributed to their different directional properties. The 31P CSA tensors exhibit considerable variations resulting in large spans of approximately 16 ppm for deltaCSA11 and approximately 22 ppm for deltaCSA22 and deltaCSA33. We examine the consequences of the CSA variations for predicting the chemical shift changes upon partial alignment deltacsa and for the values of CSA order parameters extracted from the analysis of 31P NMR relaxation data. The theoretical 31P CSA tensors as well as the experimental 31P CSA tensor of barium diethyl phosphate (BDEP) are used to calculate deltacsa for two eclipsed orientations of the CSA and molecular alignment tensors. Percentage differences between the CSA order parameters obtained using the theoretical 31P CSA tensors and the experimental 31P CSA tensor of BDEP, respectively, are also determined.

The influence of Mg2+ coordination on 13C and 15N chemical shifts in CKI1RD protein domain from experiment and molecular dynamics/density functional theory calculations

Sequence dependence of 13C and 15N chemical shifts in the receiver domain of CKI1 protein from Arabidopsis thaliana, CKI1RD, and its complexed form, CKI1RD•Mg2+, was studied by means of MD/DFT calculations. MD simulations of a 20–ns production run length were performed. Nine explicitly hydrated structures of increasing complexity were explored, up to a 40‐amino‐acid structure. The size of the model necessary depended on the type of nucleus, the type of amino acid and its sequence neighbors, other spatially close amino acids, and the orientation of amino acid NH groups and their surface/interior position. Using models covering a 10 and a 15 Å environment of Mg2+, a semi‐quantitative agreement has been obtained between experiment and theory for the V67−I73 sequence. The influence of Mg2+ binding was described better by the 15 Å as compared to the 10 Å model. Thirteen chemical shifts were analyzed in terms of the effect of Mg2+ insertion and geometry preparation. The effect of geometry was significant and opposite in sign to the effect of Mg2+ binding. The strongest individual effects were found for 15N of D70, S74, and V68, where the electrostatics dominated; for 13Cβ of D69 and 15N of K76, where the influences were equal, and for 13Cα of F72 and 13Cβ of K76, where the geometry adjustment dominated. A partial correlation between dominant geometry influence and torsion angle shifts upon the coordination has been observed. Proteins 2016; 84:686–699.

Electron Paramagnetic Resonance

This chapter opens with an account of electron paramagnetic resonance parameters ( g -tensor, hyperfine coupling tensor, zero-field splitting [ZFS] tensor) as obtained from experiments. The description of quantum chemistry starts with the nonrelativistic approach to hyperfine coupling and continues with the g -tensor theory, where the relativistic concepts are introduced. Then, relativistic contributions to the hyperfine coupling and the theory of ZFS are reviewed. The methodological aspects are introduced with very popular density functional calculations of the hyperfine coupling, followed by a short section on ab initio post-Hartree–Fock calculations of the same property. Likewise, the g -tensor and the ZFS tensor calculations are divided between “DFT” and “ab initio” subsections, including comparison of the advantages and disadvantages of the DFT and ab initio approaches. A short conclusion section summarizes the main methodological points raised throughout the text.