摘要:

It is shown in discussing problems involving magnetic relaxation in liquids that, whilst the usual Hilbert space spanned by all the eigenkets of the spin hamiltonian does not reflect any symmetry inherent in the spin system, the vector space (Liouville space) comprising all operators of the spin system does so. The transformation properties of the Liouville operator, as reflected by those of the high resolution spin hamiltonian and relaxation operators whose effects are introduced by means of Redfield relaxation theory, with respect to arbitrary rotations of the coordinate system are investigated. The use of irreducible tensor operators as a set of basis operators spanning Liouville space is stressed, since it is shown that their super-matrix elements of the Liouville operator are given by the Wigner-Eckart theorem provided that relaxation by anisotropy of the chemical shift or anisotropic random fields is absent. These arguments are independent of the fine details of molecular reorientation in the extreme narrowing approximation, since use is made of Hubbard's symmetry arguments to evaluate correlation functions. A further symmetry operation in Liouville space, that of spin inversion conjugation, is defined. These arguments are used to prove the existence of and equality of the time constants (T1andT2) describing the decays of the longitudinal and transverse magnetizations, in the extreme narrowing approximation for systems comprising any number of isochronous nuclei of any spin subject to relaxation mechanisms which are scalar contractions of irreducible spherical tensors of which the spin components operate on one nucleus only. The degree of correlation of the relaxation mechanisms at different nuclei does not enter the calculation. The inequality ofT1andT2for relaxation by anisotropy of the chemical shift is shown to arise from lack of symmetry in the hamiltonian. Non-exponential relaxation in the presence of the dipole-dipole mechanism in systems of isochronous spin-½ nuclei is discussed, the number of exponentials needed to describe the relaxation being symmetry determined. The case of three spin-½ nuclei located at the corners of an equilateral triangle is treated in detail, a previous result being corrected. Relaxation outside the extreme narrowing approximation is discussed for relaxation by chemical shift anisotropy and the quadrupole interaction. The utility of the symmetry arguments in the problem of calculating the band shapes of the resonances of spin-½ nuclei which are scalar coupled to nuclei of spin > ½ which are undergoing rapid quadrupole relaxation is discussed.

ISSN:0026-8976    

DOI:10.1080/00268977100101151

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Molecules which consist of a rigid frame ofC2vsymmetry and an invertor moving around an internal axis fixed in the frame may be considered as a specific case of semi-rigid molecules with one finite internal degree of freedom. Representative examples are ethylene imine, phosphirane, ammonia-d1, cyanoamine. For this class of molecules the solution to the quantum mechanical rotation-inversion problem is given. Starting from the classical rotation-inversion hamiltonian, the symmetry group of the problem is shown to be isomorphous toO+(3) ×V4. The kinetic energy matrix is then calculated analytically in the direct product of the bases of the symmetric rotor and the trigonometric functions. The calculation of the matrix elements, though quite complicated, is possible in closed form by complex integration. This in turn leads to a new aspect of the problem, which consists in a discussion of the zeros of the kinetic determinant |gmn| =g. The roots ofglying within the unit circle in the complex plane are shown to determine directly the asymptotic behaviour of the matrix elements. Using an appropriate function for the analytical representation of the two minima potential energy it is shown that a finite number of eigenvalues may be calculated to a precision sufficient for high-resolution microwave spectroscopy. Furthermore, selection rules and analytical expressions for electric dipole transition matrix elements are given, based on a model in which the electric dipole moment depends in a simple manner on the inversion angle. An application of the theory to the microwave spectrum of ethylene imine and cyanoamine is briefly discussed.

ISSN:0026-8976    

DOI:10.1080/00268977100101161

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The electron-nuclear double resonance in polybutadiene and polyisoprene, containing a nitroxide free radical (radical probe), has been studied. The inverse Overhauser effect, obtained by the double resonance experiments, proves the liquid-like character of these elastomers.

ISSN:0026-8976    

DOI:10.1080/00268977100101171

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The positions of the nuclear hyperfine lines in E.S.R. spectra from trimeric clusters of paramagnetic ions are discussed for the caseJ≫A.

ISSN:0026-8976    

DOI:10.1080/00268977100101181

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Relaxation in anABsystem, due to intermolecular dipole-dipole interaction is considered. The treatment implies a many-particle spin density matrix assuming its factorization. A critical analysis of the random local field (RLF) model is given. Relaxation coefficients of theABsystem are evaluated for two cases: (1) external relaxation due to interaction with an equivalent spin system; (2) relaxation caused by intermolecular interaction of identicalABsystems.

ISSN:0026-8976    

DOI:10.1080/00268977100101191

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Extensive measurements of the nuclear magnetic resonance relaxation times are reported for the proton, deuteron and phosphorus-31 resonances in a series of solutions of phosphine (PH3) in perdeuterophosphine (PD3) in the liquid and in the solid plastic crystal phase. All these measurements are interpreted in a consistent manner in terms of the molecular motion in spite of the difficulties arising from the proton/deuteron exchange. It is found that both the molecular reorientation and translation are rapid in the liquid. On solidification to the plastic crystal phase the molecular reorientational motion is little affected and is possibly more rapid than in the liquid but the translational motion is much slower. Correlation times are obtained for reorientation, molecular angular velocity and translational motion as well as estimates of the self-diffusion constant in the two states. Independent estimates of the molecular reorientational and angular velocity correlation times have been obtained. Since they are comparable in magnitude only a partial test of the Hubbard relation could be made. The31P relaxation time is spin-rotation controlled in the solid plastic crystal phase and this is the first time this has been established for this nucleus.

ISSN:0026-8976    

DOI:10.1080/00268977100101201

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

It is demonstrated that the Kubo and Tomita formalism of the line shape of magnetic resonance spectra can, contrary to previous statements, account for alternating line widths. In the course of the demonstration expressions for the line widths in the presence of general tensorial perturbations are derived.

ISSN:0026-8976    

DOI:10.1080/00268977100101211

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A formulation is given which permits the rapid mechanical computation of the three radial distribution functionsgij(r) of a binary hard-sphere mixture to any distancer, in the Percus-Yevick (P-Y) approximation. The consistency of the P-Y equation of state obtained by various methods is discussed.

ISSN:0026-8976    

DOI:10.1080/00268977100101221

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Self-consistent perturbation theory has been used to obtain the components of the nuclear magnetic shielding tensor of the hydrogen molecule at several values of the internuclear distance. A basis set consisting of 1sand 2patomic orbitals on each atom was chosen for the ground state. The perturbing magnetic field was allowed to mix in two perpendicular 2porbitals on each atom. The origin of the vector potential of the field was taken at the bond mid-point. The results show that the nuclear shielding for the field parallel or perpendicular to the bond diminishes as the bond length increases. Furthermore, the shielding with the field along the bond is greater than when the field is perpendicular to the bond, for all the bond lengths dealt with. The shielding anisotropy reaches its maximum at 0·9 A.U.

ISSN:0026-8976    

DOI:10.1080/00268977100101231

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Theoretical values of the nuclear magnetic shielding constantσvJfor each of the molecules H2, HD, HT, D2, DT and T2in their lower vibrational and rotational levels have been obtained from the results of the preceding paper. Values of the shielding constants of these compounds at temperatures in the range 0–700 K are predicted. Over the range -100 K to +200 K the shielding constant of H2gas (at low densities) falls by 0·038 p.p.m., an amount that should be measurable. For H2, D2and T2there is a significant difference between the shielding constants of theorthoandparamodifications at low temperatures. However, only for D2is it possible for the N.M.R. method, in principle, to obtain a doublet splitting. For hydrogen gas the shielding constant at 300 K is calculated to be 26·297 p.p.m. This is in satisfactory agreement with the experimental value of 26·51 (±0·33) p.p.m. The isotope shiftσ(HD)-σ(H2) is calculated to be 0·042 p.p.m. at 300 K. This agrees well with the three independent experimental values of 0·036, 0·038 and 0·040 p.p.m.

ISSN:0026-8976    

DOI:10.1080/00268977100101241

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor