Dipole-quadrupol interactions

The van der Waals interaction energy of two hydrogen atoms at large intemuclear distances is discussed by the use of a linear variation function. By including in the variation function, in addition to the unperturbed wave function, 26 terms for the dipole-dipole interaction, 17 for the dipole-quadrupole interaction, and 26 for the quadrupole-quadrupole interaction, the... 

The Dipole-Quadrupole Interaction The secular equation for the dipole-quadrupole interaction is... 

If the interaction Hamiltonian in the Coulomb term is expanded in a series about the separation vector, the first term of the expansion is a dipole-dipole interaction, the second a dipole-quadrupole interaction, etc.<4> Again reverting to a classical analog (dipole oscillators), the energy of interaction between the two dipoles is inversely proportional to the third power of the... 

Accounting for the instantaneous higher moments of the charge distributions of the atoms leads to an inverse eighth-power functional form (dipole-quadrupole interactions). The bulk dispersive potential is represented as shown by Mayer (1933) ... 

Table 5.37 Lattice energy terms for C2/c pyroxenes. Values in kJ/mole. bhf = energy of Born-Haber-Fayans thermochemical cycle U- = lattice energy Ec = coulombic energy = repulsive energy Edd = dipole-dipole interactions E q = dipole quadrupole interactions =...

As mentioned in Sect. 2.1, energy can be transferred by a dipole-quadrupole interaction if one of the dipole transitions is symmetry-forbidden [146], For completeness, the rate coefficient for diffusion and the dipole—quadrupole interaction is given. That is where... 

At this pressure, the polarizability/volume of SF CO2 is a little less than that of n-hexane, which suggests that there are other molecular interactions between CO2 and phenol blue in addition to dispersion and induction. The likely possibilities include electron donor-acceptor forces and dipole-quadrupole interactions. 

Examination of the various contributors to ES reveals that the dipole-dipole R"3 term is particularly sensitive to angular distortions. Whereas the dipole-quadrupole interactions contained in the R 4 term are also sizable, it is important to note that they behave differently depending upon which molecule is rotated. That is, the R 4 term produces a net stabilization if the donor is turned but adds to the destabilization of R-3 if the rotation occurs in the acceptor. Overall, the multipole series, truncated at R 5, provides a reasonable approximation of the full ES distortion energy, particularly at the longer distance. 

Dipole-Quadrupole Interaction. Still resorting to equation (58), with /n = 1, n = 2, the interaction of an electric dipole p, with a quadrupole 0, is of the form ... 

The above simple picture of the attractive component of intermolecular forces is certainly not complete. Since a complete electrostatic description of a molecule usually requires the introduction of higher-order moments, one must also consider the potential energy due to dipole quadrupole interactions, quadrupole-quadrupole interactions, and interactions of moments of higher order. These lead to terms proportional to and so on. Obviously, the potential energy... 

In addition to the total energy of the system, it is desirable to carry out FCI calibration studies of properties such as dipole moments, polarizabilities, and electrostatic forces. For example, in the O + OH- O + H reaction, the preferred approach of the O atom is determined by the dipole-quadrupole interaction. At long distances, this favors a collinear approach to the H atom, whereas for reaction to occur the O atom must migrate to the O end of OH. An accurate description of weakly interacting sy stems such as van der Waals complexes requires a quantitative description of dipole-induced-dipole or induced-dipole-induced-dipole interactions. Further, the dipole moment and polarizability functions of a molecule determine its infrared and Raman spectral intensities. 

Energy transfer between rare earth ions in tungstates was studied extensively by Van Uitert (37) who concluded that the dipole-dipole and dipole-quadrupole interactions predominate in this matrix. 

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. 

B. With this in mind, let us consider the two water molecules in Figure 19 at distances such that the Lennard-Jones repulsive term can be neglected and the interaction is purely electrostatic. The electrostatic energy, up to (molecular) dipole-quadrupole interactions, is given in terms of well-defined quantum mechanical observables by... 

We now embark upon one of the more difficult of the concepts to be presented. We have already presented the types of "poles" possible without defining their nature. There are a variety of electronic transitions based upon the spacial configuration of the electrons involved. These interpolar interactions are responsible for transfer of electronic energy from site to site in the lattice. As shown below, there are "dipole-dipole" interactions, i.e.- "dd" as weU as "dipole-quadrupole" interactions, i.e.-"dq". There are even "quadrupole-quadrupole transitions. I.e. "qq". 

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

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