9 research outputs found
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 HartreeâFock 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 HartreeâFock 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 10â20% 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 HartreeâFock 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 lÀrares upplevelser av hur daglig fysisk aktivitet pÄverkar dem i skolan. För att begrÀnsa studien valde jag att endast fokusera pÄ hur de pÄverkas inom ramen för en matematiklektion. Studien fokuserade pÄ tvÄ klasser i Ärskurs 6 som infört extra fysisk aktivitet inom ramen för hela skoldagen. Tidigare forskning lyfts fram och jÀmförs med resultaten i denna studie. Studiens frÄgestÀllningar besvaras genom bÄde kvalitativ metod i form av intervjuer samt kvantitativ metod i form av enkÀter. Resultatet visade ett visst stöd till den tidigare forskningen. Resultatet av studien indikerar att elever kÀnde sig lugnare efter fysisk aktivitet men Àven arbetsro, koncentration och skolprestationer upplevdes ha en viss positiv pÄverkan. Av detta resultat vÀcktes funderingar om vilket ansvar skolan har för att erbjuda extra fysisk aktivitet i skolan
Paramagnetic Enhancement of Nuclear SpinâSpin Coupling
We
present a derivation and computations of the paramagnetic enhancement
of the nuclear magnetic resonance (NMR) spinâspin 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 spinâspin 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<sup>II</sup>(acac)<sub>2</sub> complex, a CoÂ(II) pyrazolylborate
complex, and a lanthanide system, GdâDOTA. Particular attention
is paid to relativistic effects in HFC tensors, which are calculated
using two methods: a nonrelativistic method supplemented by perturbational
spinâorbit coupling corrections, and a fully relativistic,
four-component matrixâDiracâKohnâSham 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 <sup>13</sup>C<sup>13</sup>C couplings in the GdâDOTA
complex (as large as 9.4 Hz), may eventually become important
Magnetic Couplings in the Chemical Shift of Paramagnetic NMR
We
apply the KurlandâMcGarvey (<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 NiÂ(II), CoÂ(II), CrÂ(II), and
CrÂ(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
<sup>1</sup>H 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 cobaltÂ(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 CoÂ(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 sp<sup>2</sup>-hybridized graphene, as well as hydrogen
and fluorine vacancies in the sp<sup>3</sup>-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 sp<sup>2</sup>-defect
centers, in which the magnetic resonance parameters are greatly enhanced.
Slowly decaying adatom-induced magnetic resonance parameters with
the distance from the sp<sup>3</sup>-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
dynamicsâdensity functional
theory (MD/DFT) approach to reproduce sequence trend in <sup>31</sup>P chemical shifts (ÎŽP) in the backbone of nucleic acids. ÎŽP
for [dÂ(CGCGAATTCGCG)]<sub>2</sub>, 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 <sup>31</sup>P chemical shifts for two
distinct B-DNA subfamilies BI and BII, ÎŽP/BI and ÎŽP/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 ÎŽP/BI in the order of 0.4â0.5
ppm has been obtained. Weighted averages for individual <sup>31</sup>P nuclei in the studied DNA double-helix have been calculated from
ÎŽP/BI and ÎŽP/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 ÎŽP and theoretical ÎŽP 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
ÎŽP exhibit a systematic offset of ca. 11 ppm and overestimation
of
trends by a factor of ca. 1.7. When scaled accordingly, theoretical
ÎŽP/BI and ÎŽP/BII can be used to determine the expected
percentage of BII to match the experimental value of ÎŽP. As
evidenced by the calculations on snapshots from CarâParrinello
molecular dynamics, the systematic offsets of the theoretical ÎŽP
obtained by MD/DFT approach result primarily from the unrealistic
bond lengths employed by classical MD. The findings made in this work
provide structureâÎŽP 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>âČâDialkyldithiophosphate Ligands
Polycrystalline
bisÂ(dialkyldithiophosphato)ÂPtÂ(II) complexes of
the form [PtÂ{S<sub>2</sub>PÂ(OR)<sub>2</sub>}<sub>2</sub>] (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 <sup>31</sup>P and <sup>195</sup>Pt NMR spectroscopy,
to determine the influence of R to the structure of the central chromophore.
The measured anisotropic chemical shift (CS) parameters for <sup>31</sup>P and <sup>195</sup>Pt 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 spinâorbit
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 <sup>195</sup>Pt anisotropic parameters due to the high requirements posed
on the pseudopotential quality in such calculations. Though negligible
differences were found between the <sup>195</sup>Pt CS tensors with
different substituents R, the <sup>31</sup>P 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