Monopole-Dipole Interaction

Figure 1.96 Illustration of fixed dipole/monopole interactions where charges qi/-qi separated by a distance / represent the fixed dipole and and q2 is a monopole r is the distance of separation between dipole midpoint and monopole.

A FIGURE 10.8 Parameters by Eq. A.32 appearing in the derivation of the dipole-monopole interaction potential. 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

These polarity descriptors combine charge and geometry. Dipole moments are used to model dipole-monopole, dipole-dipole, dipole-induced dipole, and other interactions. Both molecular dipole (fi) as well as bond dipole moments may be defined for neutral molecules. A bond dipole moment due to atoms k and / separated by distance, rki, can be defined as (]i-The topographic electronic index defined in Eq. [12] is another measure (index) of polarity.The sum extends over the number of bonded atoms, N. ... 

Mossbauer spectroscopy senses the hyperfine interactions, which are present at the nucleus of the Mossbauer isotope. The electrical monopole interaction causes the isomer shift and the electric quadrupole interaction leads to the quadrupole splitting, which in the case of Fe causes a two-line Mossbauer pattern. The magnetic dipole interaction leads to a magnetically split six-line pattern (Figure 4). In the following text, these interactions and their deduction from Mossbauer spectra will be discussed. 

Figure 1. Hyperfine interactions for Fe nuclei, showing the nuclear energy level diagram for (a) an unperturbed nucleus (b) electric monopole interaction (isomer shift) (c) electric quadrupole interaction (quadrupole splitting) and (d) magnetic dipole interaction (hyperfine magnetic splitting). Each interaction is shown individually, accompanied by the resulting Mossbauer spectrum.

Dipole interactions are usually weaker than electrostatic monopole interactions but can dominate the intermolecular interactions within a supramolecular assembly. Diederich and coworkers have recently drawn attention onto dipole interactions, and multipolar interactions in general, in such systems based on a statistical analysis of structures [180]. 

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... 

R l term would be nonzero only if both partners were charged, with nonzero monopoles (i = /—()). An R 2 term appears in the interaction between the monopole of one O = 0) and the dipole of the other ( / = 1). The first term that occurs in the case of a pair of neutral molecules, as in the water dimer, is R 3 which corresponds to the interaction between the dipole moments of the two molecules (i = j = 1). Any nonzero monopole quadrupole terms would appear in this term as well. Dipole-quadrupole interactions die off as R 4, which would also contain charge-octapole interactions, should they exist. Just as the continuation of the multipole expansion to higher orders progressively improves the approximation of the true charge distribution of each monomer, the continuation of the R n summation yields a progressively better approximation to the true electrostatic interaction energy. 

Williams showed that an unrestricted bond dipole model gave erratic results for the bond dipole directions. To pursue the goals of chemical reasonableness and transferability, it seems appropriate to restrict the direction of the bond dipoles. The most natural direction is along the bond. Table 12 shows that restricted bond dipole models represent the electric potential about as well as monopole models. The two models also have nearly the same number of parameters. So the choice between these two models is a matter of convenience. If long distance interaction is considered, as in crystals, use may be made of the fact that dipole-dipole energy converges much faster than monopole-monopole energy. However, as mentioned above, if ions are considered, monopole interactions are still needed. Table 13 summarizes values of restricted bond dipole moments. 

The common expansion of the reciprocal distance in terms of spherical harmonics and collection of the corresponding orders (monopole, dipole, quadrupole,. .., interactions) leads to... 

The way that transition dipole moments interact together in multichro-mophore assemblies was initially examined by Kasha in his pioneering work on excitonic coupling. The original point dipole treatment was later refined by Hunter and Sanders who have developed a transition monopole treatment that allows quantitative prediction of the effects of excitonic interaction. Figure 13.4 qualitatively summarizes the nature of the absorption band shifts depending on the... 

For some reactions, it should be noted, is an overestimate. No appreciable excitation of an atom through the monopole interaction occurs before the projectile has penetrated closer to the target nucleus than the electron radius a. The appropriate distance of closest approach is in fact a a l a + For this reason it might be useful to think that distant collisions mean dipole interactions. 

The method of monopole interaction can be used for all transitions whether electrically or magnetically forbidden. In general, it will be more accurate than the electric dipole approximation, but it will also be more difficult to calculate. Moffitt (1956b) compromised by using the monopole interaction for nearest neighbors and the dipole interaction for the remainder. 

Interactions become shorter-ranged and weaker as higher multipole moments become involved. When a monopole interacts with a monopole. Coulomb s law says u r) oc r But when a monopole interacts with a distant dipole, coulombic interactions lead to u r) oc r (see Equation (21.26)). Continuing up the multipole series, two permanent dipoles that are far apart interact as u(r) oc r Such interactions can be either attractive or repulsive, depending on the orientations of the dipoles. Table 24.2 gives typical energies of some covalent bonds, and Table 24.3 compares covalent to noncovalent bond strengths. 

Fig. 2.7 Nuclear energy level scheme ( Fe) for electric monopole interaction (causing the isomer shift, left), pure magnetic dipole interaction (causing magnetic splitting, middle), and combined magnetic dipole interaction and electric quadrupole interaction right)...

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