Quadrupole interaction principles

J. Schmidt and D. Sebastiani (2005) Anomalous temperature dependence of nuclear quadrupole interactions in strongly hydrogen-bonded systems from first principles. J. Chem. Phys. 123, 074501... 

In Chapter I, we introduced the angular velocity of the magnetization around Hj in the rotating frame as u)j=yHj, in analogy with the Larmor frequency in the laboratory frame. This physical picture of the effect of Hj breaks down for 1>% when the non-zero quadrupole interaction makes the energy levels unequal. The basic principles are treated in Chapter VII, Section II.B.(c) of Abragam, 1961 (Appendix A) but our discussion relies on some lecture notes by Schmidt (1972). 

From the experimental standpoint, a system such as is well parameterized because there will, in principle, be three spectroscopic transitions from which it will be possible to determine the two NQI parameters, e Qq and q. Other spin systems, such as 0 (/ = S ), S, and Cl (/= 3/1) are more difficult to parameterize because there are fewer spectroscopic transitions than theoretical parameters, but techniques such as double resonance enable one to get the requisite information (Semin et al, 1975 Lucken, 1969b). Simple orbital descriptions of the nuclear quadrupole coupling parameters and orbital hybridization have been reported (Cotton Harris, 1966), and measures of the nuclear quadrupole interaction parameters and their tensor orientation can therefore be applied to solving problems of molecular structure and reactivity. 

Principles and Characteristics An interaction that is never directly seen in liquid spectra but that, if present, always dominates solid-state spectra is quadrupole interaction. Nuclei with I > Vi have an electric quadrupole moment Q that is a measure of the deviation of the nuclear charge distribution from spherical symmetry. Nuclei with 7 = 0, Vi do not care about electric field gradients their charge distribution is spherical. Some 74% of all NMR-active nuclei have I > V2, as listed elsewhere [763]. The nuclear electric quadrupole moment, 2, of an 7 > 1 nucleus can interact with the electronic environment near that nucleus to affect the nuclear spin angular momentum energy levels, even in zero magnetic field. Quadrupole interactions can... 

In principle we should also consider the electric quadrupole interaction. Since, however, Fe has the nuclear ground state I = j there is no quadrupole effect possible. It is a different matter, however, for the Mossbauer effect, which involves the 14.4 keV excited nuclear state where / = f. 

Secondary forces are primarily electrostatic in nature. They include the multipole interactions of which there are, in principle, an infinite number. However, in practice, only the monopoles, dipoles, and quadrupoles are important. 

The method Neglect of Diatomic Differential Overlap (NDDO) was originally developed by Pople and Beveridge [8] and Pople et al. [37]. The ZDO approximation [Eq. (26)] is only applied for orbital pairs centered at different atoms. Consequently, new types of two-center integrals appear compared to the INDO method, (pv pX) and (/t Fb v). This means that not only monopole-monopole interactions are taken into account, but also dipole and quadrupole terms. Thus, in principle, NDDO-based methods should give an improved description of long-range intra- and interm olecular... 

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