Asymmetry parameters

The microwave spectrum of isothiazole shows that the molecule is planar, and enables rotational constants and NQR hyperfine coupling constants to be determined (67MI41700>. The total dipole moment was estimated to be 2.4 0.2D, which agrees with dielectric measurements. Asymmetry parameters and NQR coupling constants show small differences between the solid and gaseous states (79ZN(A)220>, and the principal dipole moment axis approximately bisects the S—N and C(4)—C(5) bonds. 

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

Values of the total cross-section a a for A1 Ka, radiation, relative to the carbon Is level, have been calculated by Scofield [2.7], and of the asymmetry parameter /Ja by Redman et al. [2.8]. Seah and Dench [2.3] have compiled many measurements of the inelastic mean free path, and for elements the best-fit relationship they found was ... 

If the field gradient has no axial symmetry, then a more complicated expression is found, involving an asymmetry parameter which is often moderate. In particular, the study of this parameter has been useful for the determination of resonance structures and for the understanding of the bonding in solid iodine. The contribution of each of the molecular electrons to q is given by a relation of the form... 

Applications of electron propagator methods with a single-determinant reference state seldom have been attempted for biradicals such as ozone, for operator space partitionings and perturbative corrections therein assume the dominance of a lone configuration in the reference state. Assignments of the three lowest cationic states were inferred from asymmetry parameters measured with Ne I, He I and He II radiation sources [43]. 

Most valuable chemical information can be extracted from Mbssbauer parameters such as the isomer shift (5), the quadrupole splitting (AEq), the magnetic splitting (AEm), and the asymmetry parameter (n). 

Fig. 1. Schematic one-dimensional cross section through the Gibbs free energy surface G(R) of a spin-state transition system along the totally symmetric stretching coordinate. The situation for three characteristic temperatures is shown (B = barrier height, ZPE = zero-point energy, 28 = asymmetry parameter, J = electronic coupling parameter, AG° = Gh — GJ...

Here, I, I, and I are angular momentum operators, Q is the quadrupole moment of the nucleus, the z component, and r the asymmetry parameter of the electric field gradient (efg) tensor. We wish to construct the Hamiltonian for a nucleus if the efg jumps at random between HS and LS states. For this purpose, a random function of time / (f) is introduced which can assume only the two possible values +1. For convenience of presentation we assume equal... 

The off-diagonal elements are zero for this arrangement and Vxx = Vyy = — l/214z- As expected, the adopted coordinate system is a principal axes system (PAS) of the EFG, and the asymmetry parameter rj is zero. 

Since the EFG component E and the asymmetry parameter rj = (Fee Vyy)/V,. in the PAS are invariants of the EFG, the two similar arrangements of the charge q shown in Fig. 4.7a, b must produce the same quadrupole splitting (because energies do not depend on the choice of the coordinate system). 

The asymmetry parameter can be obtained from the corresponding results for the tensor components in the x- and y-directions,... 

The spectra are calculated by numerical diagonalization of the nuclear Hamiltonian (4.49) and powder summation over the distribution of the EFG for different values of the asymmetry parameter rj. The line width was 0.25 mm s h... 

An instructive description of the first-order perturbation treatment of the quadrupole interaction in Ni has been given by Travis and Spijkerman [3]. These authors also show in graphical form the quadrupole-spectrum line positions and the quadrupole-spectrum as a function of the asymmetry parameter r/ they give eigenvector coefficients and show the orientation dependence of the quadrupole-spectrum line intensities for a single crystal of a Ni compound. The reader is also referred to the article by Dunlap [15] about electric quadrupole interaction, in general. 

Fig. 7.33 Effect of a positive quadrupole interaction on the ground and first excited states of Ru. The asymmetry parameter r) is assumed to be zero. The ratio of the quadrupole moments is taken to be Q3/tJQs/2 = 3. a = e qQsn and B = e qQ a (from [124])...

Table 7.4 Quadrupole coupling constant eQV z and asymmetry parameter r) for hafnium compounds...

---