Quadruple moment

S. G. Anderson and D. P. Santry, J. Chem. Phys., 74, 5780 (1981). Nonempirical Molecular Orbital Calculations for Hydrogen-Bonded Molecular Solids Molecular Dipole and Quadruple Moments for Solid Hydrogen Fluoride and Hydrogen Chloride. 

For nuclei with /> 1, the quadrupole coupling constant is defined as the product of the nuclear quadruple moment eQ and the maximum principle value of electric field gradient tensor q. 

Ion-quadrupole interactions vary with the inverse eighth power of the separation distance and the quadrupole-quadrupole interactions vary with the inverse tenth power of the separation distance. The effect of quadruple moments on thermodynamic properties is already much less than that of dipole moments and the effect of higher multipoles is usually negligible. In general, neither ion-dipole nor dipole-dipole forces can produce long-range alignment effects in liquids. 

Results for dipole moments are shown in Table 29. ° Clearly, coupled with good basis sets, correlated methods can do quite well for this property. Elsewhere, we have used relaxed density-based CC and MBPT methods to study spin densities and the related hyperfine coupling constants to evaluate relativistic corrections (Darwin and mass-velocity term) when impor-tant and to evaluate highly accurate electric field gradients to extract nuclear quadruple moments. 

Nuclei with 7>l/2 are called quadrupolar nuclei. They have a non-spherical charge distribution, and thus give rise to non-spherical electric and magnetic fields. They are said to have a quadruple moment. The consequences are major complications in their NMR spectra manifested as severe fine broadening, shallow peaks, and difficulties with phasing and integration. 

It is fortunate that P is a dipolar nucleus. However, it is frequently bonded to quadrupolar nuclei, such as N, Co, Cu, Cu, Pd, Ir, and " Au. The magnitude of complications depends on factors such as natural abundance of the isotope, quadruple moment, and the relative receptivity. 

Homonuclear molecules, like N2 orH2, have no dipole moment, and rotational excitation is due to electron interaction with their quadruple moment Q. In this case the rotational transition takes place with a change of rotational quantum number, AJ = 2. The cross section of the rotational excitation by a low-energy electron is lower in this case (about 10 cm at e = 0.1 eV Geijoy Stein, 1955) ... 

Besides the size/shape exclusion, the nature of the interaction between gas molecule and pore surface is also important in determining the adsorption selectivity of a MOF toward a given gas. In most of the rigid MOFs, observed adsorption selectivity of CO2 over other gases can be attributed to the thermodynamic equilibrium effect or the kinetic effect in a given equilibrium time, namely the preferential adsorption (based on the interaction) but not the molecular sieving effect. In this case, the selectivity is related to adsorbate properties such as polarity, quadruple moment, and H-bonding, as weU as to the surface properties of the MOF pores. 

Dipole moments of atom-atomic complexes are now studied very well. These complexes are the simplest van der Waals complexes and, as a result, they have been studied first of aU and fully enough (see, for instance [14—21]). Particular analytical forms of dipole moments for atom-atomic complexes can be easily obtained from the general expressions of Sect. 3.1 with a given accuracy using the symmetry properties (Appendix B) of interacting atoms. In particular, Eq. (3.1.9) gives for two interacted atoms (when at least one of them has nonzero quadruple moment) the asymptotic behavior as / ". And when these atoms are in the state s (spherical symmetry) the leading term is caused only by the second... 

In nuclei without spherically constant distribution of charges, another type of hyperfine interaction, electric quadruple interaction, may occur. In this case, atoms with both an observable nuclear quadruple moment, a measure of the nuclear charge distribution s deviation from spherical symmetry, and a... 

The electric quadruple moment is a (3 x 3) second-rank tensor with elements... 

One can simplify the situation in the principal axes system with all the off-diagonal elements being zero. The quadruple moment is hence given as... 

Electric quadruple splitting is related to the electric quadruple moment, the inherited property of a certain type of atom, and the EFG, a measurement of the electric field surrounding an atom. This parameter concerns the electronic structure of the nucleus and the chemical environment and is hence quite useful for determining the fingerprint for valence and co-ordination while correlated with isomer shift, i.e. local distortions, local defects, spin reorientations, and crystal field asymmetry. ... 

Meanwhile, selectivity between H O and CO is important for using MOFs to separate CO from flue gas because a typical flue gas is saturated with water vapor. Some research work shows that a small amount of water can help enhance CO adsorption in HKUST-1 [48]. The enhanced CO uptake is caused by interactions between the quadruple moment of CO and the electric field created by the coordinated water molecules. However, further increasing the water loading on the HKUST-1 will result in considerable uncoordinated water molecules that block pore space and cause the HKUST-1 to adsorb less CO2 than the dry sample. On the other hand, Liu et al. reported that neither the HKUST-1 nor the Ni/DOBDC MOF can adsorb any significant amount of CO2 when water loadings are high, which means that the two... 

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