Nuclear tensor properties

The response of diamagnetic molecules to an external homogeneous static magnetic field B and to intramolecular permanent nuclear magnetic dipoles m / is effectively rationalized via maps of streamlines and modulus of quantum mechanical induced current densities 7 and In this chapter it is shown that the essential features of intrinsic tensor properties, magnetizability magnetic shielding at nucleus 7,... 

Equation (4.15) would be extremely onerous to evaluate by explicit treatment of the nucleons as a many-particle system. However, in Mossbauer spectroscopy, we are dealing with eigenstates of the nucleus that are characterized by the total angular momentum with quantum number 7. Fortunately, the electric quadrupole interaction can be readily expressed in terms of this momentum 7, which is called the nuclear spin other properties of the nucleus need not to be considered. This is possible because the transformational properties of the quadrupole moment, which is an irreducible 2nd rank tensor, make it possible to use Clebsch-Gordon coefficients and the Wigner-Eckart theorem to replace the awkward operators 3x,xy—(5,yr (in spatial coordinates) by angular momentum operators of the total... 

If we understand FM or magnetic properties of quark matter more deeply, we must proceeds to a self-consistent approach, like Hartree-Fock theory, beyond the previous perturbative argument. In ref. [11] we have described how the axial-vector mean field (AV) and the tensor one appear as a consequence of the Fierz transformation within the relativistic mean-field theory for nuclear matter, which is one of the nonperturbative frameworks in many-body theories and corresponds to the Hatree-Fock approximation. We also demonstrated... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

Lazzeretti and coworkers175 calculated nuclear electric and electromagnetic shielding tensors for 1 and oxirane. These properties are related to atomic polar tensors and atomic axial tensors used by infrared and VCD spectroscopists. The authors demonstrated that they could obtain fairly accurate sum rules for atomic polar tensors and atomic axial tensors with relatively little computational effort. 

The first term is the Zeeman interaction depending upon the g(RS OW, q ) tensor, external magnetic field B0 and electron spin momentum operator S the second term is the hyperfine interaction of the th nucleus and the unpaired electron, defined in terms hyperfine tensor A (Rsklw, qj) and nuclear spin momentum operator n. The following terms do not affect directly the magnetic properties and account for probe-solvent [tfprobe—solvent (Rsiow, qJ)l ld solvent-solvent //solvent ( qj)] interactions. An explicit... 

D. L. Bryce and R. E. Wasylishen, Symmetry properties of indirect nuclear spin-spin coupling tensors first-principles results for C1F3 and OF2. J. Am. Chem. Soc., 2000,122,11236-11237. 

This theory was first formulated by Stephens (1985). In his approach to go beyond the Bom-Oppenheimer approximation, Stephens mixed excited electronic states with the ground state. Though that approach seemed to call for the difficult calculation of excited electronic states, he finally arrived at expressions, that only involve ground state properties. As an example to the application of the theory Jalkanen et al. (1989b) report nuclear shielding tensors, atomic polar and axial tensors, as well as IR and VCD intensities of the ammonia isotopomer N H (NHDT) using different basis sets. 

Given the huge volume of work on the calculation of molecular properties in MO theory, it is surprising that there is so little effort in this direction within the VB area. The fact that the orbitals used in VB approaches are, as a mle, well-localised, suggests that these approaches would be very suitable for the calculation and interpretation of local properties, such as NMR shielding tensors and nuclear spin-spin coupling constants. 

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