Electrostatics multipoles

The result of the electrostatic multipole interaction is to deplete primarily the 5p-shell electrons in the I ion. The number of electrons originally in the 5p closed shell are lost to excited states. Since the 5p excitation is primarily to the 65 shell, the direct effect on the 5 electron density at the nucleus will be much smaller than the 5 density. As a result of the depletion of 5p electrons, however, the nucleus will be less shielded, and the 5 electrons will have a greater probability of being at... 

Born s idea was taken up by Kirkwood and Onsager [24,25], who extended the dielectric continuum solvation approach by taking into account electrostatic multipole moments, Mf, i.e., dipole, quadrupole, octupole, and higher moments. Kirkwood derived the general formula ... 

A factor -2 included in the last term here compensates for the use of Rydberg units and for the omission of the negative electronic charge in potential functions derived from Eq. (7.14). Hence the electrostatic multipole moments of atomic cell r/( are... 

We will return to the quadrupole interaction in following chapters, but we now re-examine the general expansion of the electrostatic interaction and, in particular, the possibility of other nuclear electrostatic multipole moments. Because our multipole expansion is performed in a coordinate system with origin at the centre of charge of the protons p in the nucleus, the nuclear electric dipole moment is zero. However, this result arises only from our choice of origin and we now show that there are much... 

Fig. 6. Electrostatic multipole expanded interaction energy between two ethene molecules for 8 different orientations at R = 12ao (ab initio results from refs. ). Fits and arc atom-atom (point dtarge) modd fits to the ab initio data 0 is a fit with the charges shifted from the nudei, 0 has the charges fixed on the nudei Also indicated is an empirical atom-atom potoitial for details seeref. ...

The atom-atom potential fitted to the ab initio data gives fairly re stic results for the equilibrium structure (unit cell parameters and molecular oriratations in the cell), the cohesion energy and the phonon frequencies of the molecular crystal. The latter have been obtained via both a harmonic and a self-consistent phonon lattice dynamics calculation and they were compared with and Raman spectra. About some of the aninncal hydrocarbon atom-atom potentials which are fitted to the crystal data, we can say that they correspond reasonably well with the ab initio results (see figs. 6, 7, 8), their main defect being an underestimate of the electrostatic multipole-multipolc interactions. 

The molecular electrostatic multipole moments here are defined following Buckingham [19] ... 

In the last 40 years, techniques to directly measure surface forces and force laws (force vs. separation distance between surfaces) have been developed such as the surface forces apparatus (SFA) [6] and AFM. Surface forces are responsible for the work required when two contacting bodies (such as an AFM tip in contact with a solid surface) are separated from contact to infinite distance. Although the physical origin of all relevant surface forces can be derived from fundamental electromagnetic interactions, it is customary to group these in categories based on characteristic features that dominate the relevant physical behavior. Thus, one speaks of ionic (monopole), dipole—dipole, ion—dipole interactions, electrostatic multipole forces (e.g., quadrupole), induced dipolar forces, van der Waals (London dispersive) interactions, hydrophobic and hydrophilic solvation, structural and hydration forces,... 

Higher and mixed multipole interactions are also always present and may play a dominant role in the absence of lower multipole moments, especially in the absence of mono- and dipoles. Note also that these electrostatic multipole interactions are purely classic and typical quantum mechanical effects (like Pauli repulsion etc.) are not captured. 

Diffuse dispersive attractions and hydrophobic effects One may easily imagine that many different, inhomogeneous electric fields are present in supramolecular assemblies. These fields induce new electric fields, which may also be decomposed into electrostatic multipoles (for instance, dipole moments may be induced depending on the strength of the inducing permanent field and the (local) polarizability of the system, which is the material specific quantity). Interactions based on these effects are usually denoted van der Waals interactions. But note that the induced fields themselves will induce new polarization effects and so on. 

Among the resonance mechanisms due to various electrostatic multipole interactions, the dipole-quadrupole interaction gave the best fit between theory and experiment. The transfer due to the exchange interaction was inferred not to be operative. It was finally concluded that the mechanism of the energy transfer between unlike trivalent rare earth ions in ionorganic solids is predominantly governed by the dipole-quadrupole interaction. 

Heteroarornatic molecules, and particularly polycyclic arenes with N, O, or S substitution for carbon, are prone to aromatic-aromatic interactions. As the size of the x-delocalized system increases, the OFF motif prevails over EF, but because the charge distribution and occurrence of dipoles and higher electrostatic multipoles can be variable in heteroaromatics, the nature of any offset between parallel planar molecules can similarly be variable. Net charges that can occur on heteroarornatic molecules also influence intermolecular energy and geometry. 

Electrostatic multipole moments of molecules, i.e., dipoles, quadrupoles, or octupoles, can also be obtained from QM wave functions. Methods like distributed multipole analysis (DMA) [84] or AIM [85] assign multipole moments to each atom or to specified sites of a molecule. The DMA method estimates multipole moments from QM wave functions and the highest obtained multipole moment depends on the basis set used. There are no limitations in this method on number or position of the multipoles anisotropic effects due to lone pairs or n electrons can also be considered. 

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