QED theory of the nuclear magnetic shielding in hydrogenlike ions

The shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions.     

Experimental and theoretical 31P and 77Se nuclear magnetic shielding tensors for bis(dineopentoxyphosphorothioyl) diselenide

An intergrown crystal of two phases of bis(dineopentoxyphosphorothioyl) diselenide 1 was investigated by goniometer ³¹P NMR. From the angular dependence of the chemical shift, the tensors of a triclinic and a monoclinic phase were determined. The principal values σ₁₁, σ₂₂, and σ₃₃ of the absolute nuclear magnetic shielding tensors for the triclinic phase are 134.1, 227.2, and 375.5 ppm and for the monoclinic phase are 132.4, 227.8, and 374.2 ppm, respectively. In both cases, the principal axis 3 of the ³¹P tensor is directed nearly along the P=S bond and the principal axis 2 is nearly perpendicular to the S=P—Se plane. Calculations of the ³¹P and ⁷⁷Se nuclear magnetic shielding tensors were performed for molecules of both phases of 1 and for model compounds by the sum-over-states density functional perturbation theory IGLO method. The rms distances between calculated and experimental ³¹P NMR icosahedral tensor values σ_j(j = 1,…,6) amount to 17–21 ppm. The calculated and experimental orientations of the ³¹P principal axes show a maximum difference of 5° and rms distances of 3.2 and 3.3°. For the principal value σ₃₃ of the selenium shielding tensor the agreement between calculated and experimental values is satisfactory, but the calculated values σ₁₁ and σ₂₂ are distinctly too small. Calculations for a model compound in which the methyl groups of the neopentoxy residue are substituted by protons lead practically to the same results.     

Gauge invariance and average excitation energy approximation in the theory of nuclear magnetic shielding

The effects of three-body non-additivities on the most stable structures of Ar⁺ _n (3 ≤ n ≤ 27) clusters have been investigated in an extended diatomics-in-molecules (DIM) approach. Non-additive interaction terms for both the neutral and the ionic trimer have been included explicitly in the DIM Hamiltonian. Structural rearrangement is observed for a number of cluster sizes due to induced dipole—induced dipole interactions.     

Paramagnetic vortices and proton magnetic shielding in aromatic molecules

Summary By means of symmetry considerations it is shown that aromatic hydrocarbons, perturbed by a magnetic field perpendicular to the molecular plane, are characterized by an interatomic paramagnetic circulation of electrons, flowing around the highest symmetry axis, which is related to the nodal topology of the wave function. An actual calculation confirms that the field of quantum-mechanical current density presents an axial vortex due to σ electrons in benzene, which overcomes the diamagnetic π streamlines. The analysis of the orbital contributions to proton nuclear shielding reveals that σ electrons cause low field shifts, in the NMR spectrum, comparable in magnitude with those arising from π circulation. These results would imply the need for modifying some features of London's ring current model.

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Riassunto Per mezzo di considerazioni topologiche si dimostra che il benzene ed altre molecole aromatiche, perturbate da un campo magnetico perpendicolare al piano molecolare, sono caratterizzate da una corrente interatomica paramagnetica di elettroni σ, che circolano in un vortice attorno all'asse principale di simmetria. Un calcolo accurato della densità di corrente quantomeccanica nell'approssimazione Hartree-Fock conferma l'esistenza del vortice paramagnetico al centro del benzene. L'analisi dei contributi orbitalici al tensore di schermo magnetico al protone rivela che gli elettroni σ causano spostamenti a campo basso nello spettro NMR confrontabili con quelli dovuti alla circolazione diamagnetica degli elettroni π. Questi risultati sembrano implicare la necessità di rivedere alcuni aspetti del modello a correnti di anello di London.

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Резюме С помощью топологических рассмотрений показывается, что бензол и другие ароматические молекулы, возмущенные магнитным полем, перпендикулярным к плоскости молекулы, характеризуются парамагнитным межатомным током электронов σ, которые циркулируют в вихре вокруг главной оси симметрии. Точное вычисление плотности квантовомеханического тока в приближении Хартри-Фока подтверждает существование парамагнитного вихря в центре бензола. Анализ орбитальных вкладов в тензор магнитного экранирования протона показывает, что электроны σ вызывают сдвит слабого поля, в спектре ЯМР, сравнимый со сдвигом, обусловленным диамагнитной циркуляцией электронов π. Полученные результаты указывают на необходимость пересмотва некоторых аспектов модели кольцевых токов Лондона.

     

Asymmetry in the nuclear magnetic shielding tensor

The applicability of Green's function (GF) and Feynman path-integral quantum Monte Carlo (QMC) methods for the simulation of cyclic networks with (4n + 2) and 4n (n = 1, 2, 3, …) electrons is analysed. Both QMC techniques are employed in simulations on the basis of the simple Hückel Hamiltonian which is exclusively defined by nearest-neighbour hopping elements. In addition we have used the Pariser-Parr-Pople (PPP) Hamiltonian to perform GF QMC simulations. The electronic energies E derived by the QMC methods are compared either with Hückel molecular orbital (HMO) results or exact configuration interaction data where (π) electronic correlations are fully taken into account. A sign problem occurs in QMC simulations of 4n annulenes. This leads to an error in the total energy in the standard formulations of the employed QMC techniques, which is enhanced with decreasing ring size. A simple modification in the QMC formalisms is suggested to avoid the numerical uncertainties caused by the sign problem in 4n annulenes. Renormalization of the kinetic hopping integrals t by t cos (π/M) with M abbreviating the number of atomic sites leads to ground state energies as well as any other quantity close to the values derived by conventional diagonalization techniques. Substitution of t against t cos (π/M) conserves a common sign of all matrix elements containing the hopping. The occurrence of negative probabilities, which lead to numerical problems in the QMC simulations, is thereby prevented. The transformation suggested in 4n rings has a formal connection to so-called Möbius rings.     

Nuclear spin relaxation and magnetic shielding tensors of atoms constituting cyanogen bromide molecule

The temperature dependence of the correlation time describing reorientation kinetics of cyanogen bromide in CDCl₃ solution has been determined on the basis of the linewidths of the ¹⁴N NMR signal. It has been found that the longitudinal spin relaxation of the ¹⁵N nucleus occurs by shielding anisotropy and spin-rotation mechanisms, whereas for the ¹³C nucleus these mechanisms are of lesser importance. In the latter case the scalar relaxation of the second kind due to carbon-bromine coupling is the predominant relaxation mechanism. The parameter values: ¹ J(¹³C—⁷⁹Br) = 349 ± 10 Hz, T ₁ (⁷⁹Br, 303 K) = 2.31 ± 0.22 × 10^?7 s, Δσ(¹⁵N) = 565 ± 16 ppm and Δσ(¹³C) = 276 ± 120 ppm have been determined from the relaxation data analysis. The shielding anisotropy parameters Δσ(¹⁵N) = 580 ± 50 ppm and Δσ(¹³C) = 274 ± 9 ppm have been independently determined using ¹³C and ¹⁵N NMR in liquid crystalline solvent. The experimentally determined shielding tensors for sp-hybridized atoms in the investigated compound and in a series of bromoacetylenes have been compared with the results of quantum mechanical calculations [GIAO, DFT B3LYP/6-311 + +G(2d,p)]. The ‘heavy atom effect’ shielding bromine-bonded carbons is of the order of — 25 ppm and concerns mainly the σ⊥ component.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

The reaction field contribution to the proton magnetic shielding of acetonitrile in some non-polar solvents

The gas-to-infinite dilution proton chemical shifts of acetonitrile in a series of non-polar, isotropic solvents have been measured. After allowance for the bulk susceptibility and van der Waals contributions, it is possible to to explain the observed shifts by the well-known reaction field theory. The existing level of experimental error in chemical shift measurement is sufficiently large that no justification exists in preferring the form of the theory based on an ellipsoidal cavity to that based on a spherical cavity. Some further observed results are given which demonstrate the existence of specific interactions between acetonitrile and each of several non-polar solvents including carbon tetrachloride.     

Nuclear magnetic shielding tensors of207Pb2+ in Pb(NO3)2

The NMR signals of²⁰⁷Pb were observed in a single crystal of Pb(NO₃)₂ and could be assigned to the four different Pb²⁺ sites by the dependence of the linewidths on the orientation. Four different nuclear magnetic shielding tensors with equal principal values but with different characteristic vectors could be determined. The symmetry of the shielding tensors is in agreement with the symmetry at the Pb²⁺ sites. It is shown, that intermolecular contributions can not account for the anisotropy of the nuclear magnetic shielding, which is 3 of the isotropic absolute magnetic shielding.     

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for ¹³C and ¹⁵N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.     

核磁共振实验测量方法的分析

对测量氢核、氟核的g因子等实验过程进行原理分析,给出了10 ms等间隔测量法和利萨如图形测量法的合理解释.     

Fiber-to-field angle dependence of proton nuclear magnetic relaxation in collagen

Longitudinal and transverse proton relaxation times were measured on pig tendon. For T₁, dispersion curves and more accurate measurements at 20 MHz are presented. Values of T₂ were obtained from CPMG pulse sequences, at 20 MHz. The dependence of relaxation times against the fiber-to-field angle was particularly investigated. Longitudinal relaxation rate was found to be almost orientation independent, and presented quadrupolar peaks between 1 and 4 MHz. On the contrary, transverse relaxation, that was well fitted by the sum of four exponentials, was highly orientation dependent. Deconvolution showed that the exponentials decaying most quickly are most orientation dependent. For those two fractions, a cross-relaxation model allowed explaining the fiber-to-field angle dependence, and the specially low rate corresponding to the magic angle of 55°. Finally, each decaying mode was assigned to a fraction of protons localized in the macromolecular structure and characterized by particular dynamics.     

The signal-to-noise ratio of the nuclear magnetic resonance experiment. 1976

A fresh approach to the calculation of signal-to-noise ratio, using the Principle of Reciprocity, is formulated. The method is shown, for a solenoidal receiving coil, to give the same results as the traditional method of calculation, but its advantage lies in its ability to predict the ratio for other coil configurations. Particular attention is paid to the poor performance of a saddle-shaped (or Helmholtz) coil. Some of the practical problems involved are also discussed, including the error of matching the probe to the input impedance of the preamplifier.     

核磁共振实验教学内容的重组与优化

探索研究了一种将连续核磁共振和脉冲核磁共振有机融合的实验教学方法.在实验中,利用多媒体课件展示核磁共振的物理原理,学生分别采用连续和脉冲核磁共振方法测量同样浓度的CuSiO4水溶液的表观弛豫时间和横向弛豫时间,了解样品浓度、磁场非均匀度等因素对横向弛豫时间测量的影响.     

High resolution nuclear magnetic resonance spectroscopy in liquids and gases at pressures up to 2500 bar: II. Density dependence of the proton magnetic shielding constants in the nonpolar gases methane and ethylene

The density dependence of the proton magnetic shielding constant σ in methane and ethylene has been investigated experimentally using a high resolution spectrometer which operates with hydrostatic pressures between 0 and 2500 bar. At a constant temperature of 29.2°C a nonlinear dependence of σ on the density ? has been observed for both CH₄ and C₂H₄ in density intervals from 0–575 amagat and 0–475 amagat, respectively. Using the same apparatus the diamagnetic molar susceptibilities of the two gases have also been determined. The experimental results are discussed theoretically by comparing the observed variations of the shielding constants to the values calculated with theoretical models taken from literature.