spin–orbit coupling
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ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.
- Publikační typ
- časopisecké články MeSH
Enhancing cognitive functions through noninvasive brain stimulation is of enormous public interest, particularly for the aging population in whom processes such as working memory are known to decline. In a randomized double-blind crossover study, we investigated the acute behavioral and neural aftereffects of bifrontal and frontoparietal transcranial direct current stimulation (tDCS) combined with visual working memory (VWM) training on 25 highly educated older adults. Resting-state functional connectivity (rs-FC) analysis was performed prior to and after each stimulation session with a focus on the frontoparietal control network (FPCN). The bifrontal montage with anode over the left dorsolateral prefrontal cortex enhanced VWM accuracy as compared to the sham stimulation. With the rs-FC within the FPCN, we observed significant stimulation × time interaction using bifrontal tDCS. We found no cognitive aftereffects of the frontoparietal tDCS compared to sham stimulation. Our study shows that a single bifrontal tDCS combined with cognitive training may enhance VWM performance and rs-FC within the relevant brain network even in highly educated older adults.
- MeSH
- čelní lalok MeSH
- dvojitá slepá metoda MeSH
- klinické křížové studie MeSH
- kognice * MeSH
- kognitivně behaviorální terapie metody MeSH
- krátkodobá paměť MeSH
- lidé MeSH
- magnetická rezonanční tomografie MeSH
- neuropsychologické testy MeSH
- prefrontální mozková kůra MeSH
- přímá transkraniální stimulace mozku metody MeSH
- psychomotorický výkon MeSH
- senioři MeSH
- stupeň vzdělání MeSH
- temenní lalok MeSH
- Check Tag
- lidé MeSH
- mužské pohlaví MeSH
- senioři MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- randomizované kontrolované studie MeSH
Three-dimensional topological insulators are an important class of modern materials, and a strong spin-orbit coupling is involved in making the bulk electronic states very different from those near the surface. Bi2Se3 is a model compound, and 209Bi NMR is employed here to investigate the bulk properties of the material with focus on the quadrupole splitting. It will be shown that this splitting measures the energy band inversion induced by spin-orbit coupling in quantitative agreement with first-principle calculations. Furthermore, this quadrupole interaction is very unusual as it can show essentially no angular dependence, e.g., even at the magic angle the first-order splitting remains. Therefore, it is proposed that the magnetic field direction is involved in setting the quantization axis for the electrons, and that their life time leads to a new electronically driven relaxation mechanism, in particular for quadrupolar nuclei like 209Bi. While a quantitative understanding of these effects cannot be given, the results implicate that NMR can become a powerful tool for the investigation of such systems.
- Publikační typ
- časopisecké články MeSH
... Structure of molecules 80 -- Introduction 80 -- Electrons occupy atomic orbitals 83 -- Molecular orbitals—diatomic ... ... molecules 88 -- Bonds between different atoms 95 -- Hybridization of atomic orbitals 99 -- Rotation ... ... arrows 120 -- Further reading 124 itk Nucleophilic addition to the carbonyl group 125 -- Molecular orbitals ... ... to oxygen 281 -- Protons on heteroatoms have more variable shifts than protons on carbon 282 -- Coupling ... ... 78 -- The Heck reaction couples together an organic halide or triflate and an alkene 1079 -- Cross-coupling ...
Second edition xxv, 1234 stran : ilustrace ; 28 cm
- Konspekt
- Organická chemie
- NLK Obory
- chemie, klinická chemie
- NLK Publikační typ
- učebnice vysokých škol
Reduction potentials of several M(2+/3+) (M = Ru, Os) octahedral complexes, namely, [M(H2O)6](2+/3+), [MCl6](4-/3-), [M(NH3)6](2+/3+), [M(en)3](2+/3+) [M(bipy)3](2+/3+), and [M(CN)6](4-/3-), were calculated using the CASSCF/CASPT2/CASSI and MRCI methods including spin-orbit coupling (SOC) by means of first-order quasi-degenerate perturbation theory. It was shown that the effect of SOC accounts for a systematic shift of approximately -70 mV in the reduction potentials of the studied ruthenium (II/III) complexes and an approximately -300 mV shift for the osmium(II/III) complexes. SOC splits the sixfold-degenerate (2)T(2g) ground electronic state (in ideal octahedral symmetry) of the M(3+) ions into the E((5/2)g) Kramers doublet and G((3/2)g) quartet, which were calculated to split by 1354-1573 cm(-1) in the Ru(3+) complexes and 4155-5061 cm(-1) in the Os(3+) complexes. It was demonstrated that this splitting represents the main contribution to the stabilization of the M(3+) ground state with respect to the closed-shell (1)A(1g) ground state in M(2+) systems. Moreover, it was shown that the accuracy of the calculated reduction potentials depends on the calculated solvation energies of both the oxidized and reduced forms. For smaller ligands, it involves explicit inclusion of the second solvation sphere into the calculations, whereas implicit solvation models yield results of sufficient accuracy for complexes with larger ligands. In such cases (e.g., [M(bipy)3](2+/3+) and its derivatives), very good agreement between the calculated (SOC-corrected) values of the reduction potentials and the available experimental values was obtained. These results led us to the conclusion that especially for Os(2+/3+) complexes, inclusion of SOC is necessary to avoid systematic errors of approximately 300 mV in the calculated reduction potentials.
... PREFACE xxvii -- INTRODUCTION xxxii -- CHAPTER 1 -- CHEMICAL BONDING 6 -- 1.1 Atoms, Electrons, and Orbitals ... ... Simple Molecules 26 -- Molecular Models 27 -- 1.11 Molecular Dipole Moments 29 -- 1.12 Molecular Orbitals ... ... 13.6 Chemical Shift and Molecular Structure 519 -- 13.7 Interpreting Proton NMR Spectra 521 -- 13.8 Spin-Spin ... ... Splitting in NMR Spectroscopy 525 -- 13.9 Patterns of Spin-Spin Splitting: The Ethyl Group 528 -- 13.10 ... ... Patterns of Spin-Spin Splitting: The Isopropyl Group 530 -- 13.11 Patterns of Spin-Spin Splitting: Pairs ...
3rd ed. 1151, [150] s., tab., vzorce
