Dipole-quadrupole

V — (dipole-dipole + dipole-quadrupole + dipole-octopo e,etc.)... 

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

The quadrupole-dipole interaction differs by a factor of 2 from the usual definition of this term.48 However, the effect of this difference on the overall results of the simulation that it was used in is thought to be small. The sign of Q was taken as positive and the dipole moment direction was from the oxygen atom to the carbon atom.50... 

Table 7 Typical calculated bond dipoles and quadrupoles. Dipole moments are given in Debyes, quadrupole moments in Buckinghams. The positive direction for dipole is defined to be from the heavy atom outwards, and quadrupole moments are calculated with respect to the mid-point of the bond...

The leading term in the interaction between positronium and a charged particle is the usual 1/R4 polarization potential, where R is the coordinate of the centre of mass of the positronium relative to the other particle. If, however, positronium interacts with a neutral atom or another positronium, the interaction is dominated by the van der Waals potential arising from the induced dipole-dipole and quadrupole-dipole terms, which has the long-range form... 

In the region of negligible overlap, the three-body interactions can be calculated, just like the two-body ones, from imaginary frequency polarizabilities. This has been done, for example, by Doran78 for interaction of triplets of noble-gas atoms. He gives the coefficients for dipole-dipole-dipole, dipole-dipole-quadrupole, dipole-quadru-pole-quadrupole, quadrupole-quadrupole-quadrupole, and dipole-dipolc-octupole terms. 

Figure 3.26. A quadrupole-dipole separated local field experiment for the OH group in Mg(OH)x(OCH3)2-x with A. the experimental data compared with B. the simulation of the intensity assuming the tensors are collinear from van Eck and Smith (1998) with permission...

Qualitative evaluation (attractive or repulsive) is made of the dipole-dipole (R 3), dipole-quadrupole plus quadrupole-dipole (R 4), and quadrupole-quadrupole (R 5) electrostatic interactions for the different angular geometries of the dimer. 

Figure 5.4(a), strong

For complexes between C2H2 and HF, the model correctly predicts the T-shaped C2 structure of the dimer (Figure 5.1e), having the proton of the proton-donor HF molecule directly H-bonded to the n bond of acetylene, be more stable than the linear CooV structure, where acetylene would act as proton donor in forming a H-bonded structure with the a lone pair of fluorine. In the first case, in fact, both quadrupole-dipole (R-4) and quadrupole-quadrupole (R 5)na interactions are attractive. 

It is therefore necessary to sum the amplitudes, taking into account the possible presence of a quadrupole/dipole mixing ratio of 8 and a phase factor between these of e . Discussions of various aspects of the theory are available [34-38]. The amplitude a is proportional to... 

The method used here for considering conformal solution models for fluids with molecular anisotropies is based on the method used by Smith (4) for treating isotropic one-fluid conformal solution methods as a class of perturbation methods. The objective of the method is to closely approximate the properties of a mixture by calculating the properties of a hypothetical pure reference fluid. The characterization parameters (in this case, intermolecular potential parameters) of the reference fluid are chosen to be functions of composition (i.e., mole fractions) and the characterization parameters for the various possible molecular pair interactions (like-like and unlike-unlike). In principle, all molecular anisotropies (dipole-dipole, quadrupole-quadrupole, dipole-quadrupole, and higher multipole interactions, as well as overlap and dispersion interactions ) can be included in the method. Here, the various molecular anisotropies are lumped into a single term, so that the intermolecular potential energy uy(ri2, on, a>2) between Molecules 1 and 2 of Species i and / can be written in the form... 

It is not clear, therefore, whether the long-range attractive quadrupole-dipole term of the interaction potential is the major factor in this E V transfer. 

Pritt and Coombe and Donovan, Fotakis, and Golde have extended the ideas behind the Ewing theory to cover the case of quadrupole-dipole attractive forces, which vary as R . This is exactly the type of force for which Sharma and Brau originally performed the perturbation theory calculation. For small values of wb/v the cross-section averaged over temperature and impact parameter is given by ... 

Fried and Hu used MP2 calculations (6-31-r+G basis set) in an effort to identify the nature of spedfic interactions between CO2 and fluorinated substituent groups on polymers [20]. They reported that quadrupole-dipole interactions are important contributors to the total energy of interaction. In experimental studies by McHugh et al., the favorable misdbihty of fluorocarbons has also been attributed to polar-quadrupole interactions [21]. The authors noted that fluorination imparts solubihty to the polymer provided that polarity is also introduced to the polymer via such fluorination. Too high a level of fluorination produces an adverse effect on miscibihty due to dominance of dipole-dipole interactions between the polymer chains [22]. 

Fig. 2.2 A quadrupole-dipole transform in the transition from the (2,1,1) level to the (1,1,1) level in QDb- Such a transform is unachievable without the optical near-field interactions between QDa and QDb, which allow the (2,1,1) level in QDb to be populated with excitons...

---