Fully Relativistic Calculations of Faraday and Nuclear Spin-Induced Optical Rotation in Xenon

Nuclear spin-induced optical rotation (NSOR) arising from the Faraday effect may constitute an advantageous novel method for the detection of nuclear magnetization. We present first-principles nonrelativistic and relativistic, two- and four-component, basis-set limit calculations of this phenomenon for xenon. It is observed that only by utilization of relativistic methods may one qualitatively reproduce experimental liquid-state NSOR data. Relativistic effects lower the results by 50% as compared to nonrelativistic values. Indeed, relativistic Hartree–Fock calculations at the four-component or exact two-component (X2C) level account for the discrepancy between experimental results and earlier nonrelativistic theory. The nuclear magnetic shielding constant of traditional nuclear magnetic resonance as well as the Verdet constant parametrizing optical rotation due to an external magnetic field were also calculated. A comparison between results obtained using Hartree–Fock and density-functional theory methods at relativistic and nonrelativistic levels, as well as coupled cluster methods at the nonrelativistic level, was carried out. Completeness-optimized basis sets were employed throughout, for the first time in fully relativistic calculations. Full relativity decreases the Verdet constant by 4%. X2C theory decreases the absolute value of NSOR by 10–20% as compared to the four-component data, while for Verdet constants, the results are only slightly smaller than the fully relativistic values. For both properties, two-component calculations decrease the computational time by roughly 90%. Density-functional methods yield substantially larger values of NSOR than the Hartree–Fock theory or experiments. Intermolecular interactions are found to decrease NSOR and, hence, compensate for the electron correlation effect

Physical activity in school

Syftet med denna studie var att belysa elever och lärares upplevelser av hur daglig fysisk aktivitet påverkar dem i skolan. För att begränsa studien valde jag att endast fokusera på hur de påverkas inom ramen för en matematiklektion. Studien fokuserade på två klasser i årskurs 6 som infört extra fysisk aktivitet inom ramen för hela skoldagen. Tidigare forskning lyfts fram och jämförs med resultaten i denna studie. Studiens frågeställningar besvaras genom både kvalitativ metod i form av intervjuer samt kvantitativ metod i form av enkäter. Resultatet visade ett visst stöd till den tidigare forskningen. Resultatet av studien indikerar att elever kände sig lugnare efter fysisk aktivitet men även arbetsro, koncentration och skolprestationer upplevdes ha en viss positiv påverkan. Av detta resultat väcktes funderingar om vilket ansvar skolan har för att erbjuda extra fysisk aktivitet i skolan

Paramagnetic Enhancement of Nuclear Spin–Spin Coupling

We present a derivation and computations of the paramagnetic enhancement of the nuclear magnetic resonance (NMR) spin–spin coupling, which may be expressed in terms of the hyperfine coupling (HFC) and (for systems with multiple unpaired electrons) zero-field splitting (ZFS) tensors. This enhancement is formally analogous to the hyperfine contributions to the NMR shielding tensor as formulated by Kurland and McGarvey. The significance of the spin–spin coupling enhancement is demonstrated by using a combination of density-functional theory and correlated <i>ab initio</i> calculations, to determine the HFC and ZFS tensors, respectively, for two paramagnetic 3d metallocenes, a Cr^II(acac)₂ complex, a Co­(II) pyrazolylborate complex, and a lanthanide system, Gd–DOTA. Particular attention is paid to relativistic effects in HFC tensors, which are calculated using two methods: a nonrelativistic method supplemented by perturbational spin–orbit coupling corrections, and a fully relativistic, four-component matrix–Dirac–Kohn–Sham approach. The paramagnetic enhancement lacks a direct dependence on the distance between the coupled nuclei, and represents more the strength and orientation of the individual hyperfine couplings of the two nuclei to the spin density distribution. Therefore, the enhancement gains relative importance as compared to conventional coupling as the distance between the nuclei increases, or generally in the cases where the conventional coupling mechanisms result in a small value. With the development of the experimental techniques of paramagnetic NMR, the more significant enhancements, e.g., of the ¹³C¹³C couplings in the Gd–DOTA complex (as large as 9.4 Hz), may eventually become important

Magnetic Couplings in the Chemical Shift of Paramagnetic NMR

We apply the Kurland–McGarvey (<i>J. Magn. Reson.</i> <b>1970</b>, <i>2</i>, 286) theory for the NMR shielding of paramagnetic molecules, particularly its special case limited to the ground-state multiplet characterized by zero-field splitting (ZFS) interaction of the form <b><i>S</i></b>·<b><i>D</i></b>·<b><i>S</i></b>. The correct formulation for this problem was recently presented by Soncini and Van den Heuvel (<i>J. Chem. Phys.</i> <b>2013</b>, <i>138</i>, 054113). With the effective electron spin quantum number <i>S</i>, the theory involves 2<i>S</i>+1 states, of which all but one are low-lying excited states, between which magnetic couplings take place by Zeeman and hyperfine interactions. We investigate these couplings as a function of temperature, focusing on both the high- and low-temperature behaviors. As has been seen in work by others, the full treatment of magnetic couplings is crucial for a realistic description of the temperature behavior of NMR shielding up to normal measurement temperatures. At high temperatures, depending on the magnitude of ZFS, the effect of magnetic couplings diminishes, and the Zeeman and hyperfine interactions become effectively averaged in the thermally occupied states of the multiplet. At still higher temperatures, the ZFS may be omitted altogether, and the shielding properties may be evaluated using a doublet-like formula, with all the 2<i>S</i>+1 states becoming effectively degenerate at the limit of vanishing magnetic field. We demonstrate these features using first-principles calculations of Ni­(II), Co­(II), Cr­(II), and Cr­(III) complexes, which have ZFS of different sizes and signs. A non-monotonic inverse temperature dependence of the hyperfine shift is predicted for axially symmetric integer-spin systems with a positive <i>D</i> parameter of ZFS. This is due to the magnetic coupling terms that are proportional to <i>kT</i> at low temperatures, canceling the Curie-type 1/<i>kT</i> prefactor of the hyperfine shielding in this case

¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study

We apply the theory of the nuclear magnetic resonance (NMR) chemical shift for paramagnetic systems to demanding cobalt­(II) complexes. Paramagnetic NMR (pNMR) chemical shift results by density-functional theory (DFT) can be very far from the experimental values. Therefore, it is of interest to investigate the applicability of electron-correlated <i>ab initio</i> computational methods to achieve useful accuracy. Here, we use <i>ab initio</i> wave function based electronic structure methods to calculate the pNMR chemical shift within the theoretical framework established recently. We applied the <i>N</i>-electron valence-state perturbation theory (NEVPT2) on three Co­(II) systems, where the active space of the underlying complete active space self-consistent field (CASSCF) wave function consists of seven electrons in the five metal 3<i>d</i> orbitals. These complexes have the <i>S</i> = 3/2 electronic ground state consisting of two doublets separated by zero-field splitting (ZFS). To calculate the hyperfine coupling tensor <b><i>A</i></b>, DFT was used, while the <i><b>g</b></i>- and ZFS-tensors were calculated using the <i>ab initio</i> CASSCF and NEVPT2 methods. These results were combined to obtain the total chemical shifts. The shifts obtained from these calculations are in generally good agreement with the experimental results, in some cases suggesting a reassignment of the signals. The accuracy of this mixed <i>ab initio</i>/DFT approach is very promising for further applications to demanding pNMR problems involving transition metals

Spin Doublet Point Defects in Graphenes: Predictions for ESR and NMR Spectral Parameters

An adatom on a graphene surface may carry a magnetic moment causing spin-half paramagnetism. This theoretically predicted phenomenon has recently also been experimentally verified. The measurements of defect-induced magnetism are mainly based on magnetometric techniques where artifacts such as environmental magnetic impurities are hard to rule out. Spectroscopic methods such as electron spin resonance (ESR) and paramagnetic nuclear magnetic resonance (pNMR) are conventionally used in the development of magnetic materials, <i>e.g.</i>, to study paramagnetic centers. The present density functional theory study demonstrates with calculations of the ESR <b>g</b>-tensor and the hyperfine coupling tensors, as well as the pNMR shielding tensor, that these spectroscopies can be used to identify the paramagnetic centers in graphenes. The studied defects are hydrogen and fluorine adatoms on sp²-hybridized graphene, as well as hydrogen and fluorine vacancies in the sp³-hybridized graphane and fluorographene, respectively. The directly measurable ESR and pNMR parameters give insight into the electronic and atomic structures of these defects and may contribute to understanding carbon-based magnetism via the characterization of the defect centers. We show that missing hydrogen and fluorine atoms in the functionalized graphane and fluorographene, respectively, constitute sp²-defect centers, in which the magnetic resonance parameters are greatly enhanced. Slowly decaying adatom-induced magnetic resonance parameters with the distance from the sp³-defect, are found in pure graphene

Observation of Optical Chemical Shift by Precision Nuclear Spin Optical Rotation Measurements and Calculations

Nuclear spin optical rotation (NSOR) is a recently developed technique for detection of nuclear magnetic resonance via rotation of light polarization, instead of the usual long-range magnetic fields. NSOR signals depend on hyperfine interactions with virtual optical excitations, giving new information about the nuclear chemical environment. We use a multipass optical cell to perform the first precision measurements of NSOR signals for a range of organic liquids and find clear distinction between proton signals for different compounds, in agreement with our earlier theoretical predictions. Detailed first-principles quantum mechanical NSOR calculations are found to be in agreement with the measurements

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 ³¹P 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 ³¹P 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 ³¹P 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

Experimental and First-Principles NMR Analysis of Pt(II) Complexes With <i>O</i>,<i>O</i>′‑Dialkyldithiophosphate Ligands

Polycrystalline bis­(dialkyldithiophosphato)­Pt­(II) complexes of the form [Pt­{S₂P­(OR)₂}₂] (R = ethyl, <i>iso</i>-propyl, <i>iso</i>-butyl, <i>sec</i>-butyl or <i>cyclo</i>-hexyl group) were studied using solid-state ³¹P and ¹⁹⁵Pt NMR spectroscopy, to determine the influence of R to the structure of the central chromophore. The measured anisotropic chemical shift (CS) parameters for ³¹P and ¹⁹⁵Pt afford more detailed chemical and structural information, as compared to isotropic CS and <i>J</i> couplings alone. Advanced theoretical modeling at the hybrid DFT level, including both crystal lattice and the important relativistic spin–orbit effects qualitatively reproduced the measured CS tensors, supported the experimental analysis, and provided extensive orientational information. A particular correction model for the non-negligible lattice effects was adopted, allowing one to avoid a severe deterioration of the ¹⁹⁵Pt anisotropic parameters due to the high requirements posed on the pseudopotential quality in such calculations. Though negligible differences were found between the ¹⁹⁵Pt CS tensors with different substituents R, the ³¹P CS parameters differed significantly between the complexes, implying the potential to distinguish between them. The presented approach enables good resolution and a detailed analysis of heavy-element compounds by solid-state NMR, thus widening the understanding of such systems