Dipole-quadrupole forces

COEKKICIENTS FOR THE INDUCED DiPOLE-DiPOLE AND DiPOLE-QuADRUPOLE FoRCES... 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

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. 

We will find in this section that different electrostatic intermolecular forces, e.g. dipole-dipole, quadrupole-quadrupole, van der Waals, and acceptor-donor interactions contribute to chiral recognition. Most important, however, are hydrogen bonding and steric interactions. 

The Direct Lattice Sum. Dispersion forces between two atoms can be described by a potential function expressed in terms containing inverse powers of the internuclear separations, s. The simplest function of this sort includes a potential energy of attraction proportional to the inverse sixth power of the separation and a repulsion that is zero at distances of separation greater than a particular value se and infinite at separations less than sc. This is the so-called hard sphere or van der Waals model. Such an approximate potential function can be improved in two respects. Investigations of the second virial coefficient have revealed that the potential energy of repulsion is best described as proportional to the inverse twelfth power of the separation and the term in sr9, which accounts for the greater part of the total attraction potential, due to the attraction of mutually induced dipoles, should have added to it the dipole-quadrupole and quadrupole-quadru-pole attractions, expressed as terms in sr8 and s-10, respectively. The complete potential function for the forces between two atoms is, therefore ... 

An important point to recall regarding the dissolution of an ionic crystal (Chapter 2) is that ionic lattices consist of ions even before they come in contact with a solvent. In fact, all that a polar solvent does is to use ion-dipole (or ion-quadrupole) forces to disengage the ions from the lattice sites, solvate them, and disperse them in solution. 

This equation was first used by Born, Huggins, and Meyer and therefore bears their names. The first two terms represent, respectively, the attractive and repulsive potentials. The last two terms represent dipole-dipole and dipole-quadrupole potentials, respectively. In spite of allowing for the dipole interactions, the calculation is still a hard-sphere one, a mean spherical approximation, because the forces are not allowed to change the shape and the position of the particles. Later on, Saboungi et al. 

Water, it may be recalled (Chapters 2 and 4), has two modes of solvent action, depending on the nature of the added electrolyte. The water can contact an ionic crystal (e.g., NaCl), detach the ions from the lattice through the operation of ion-dipole (or ion-quadrupole) forces, and convert them to hydrated ions (Chapter 2). 

The narrow absorption and emission bands of rare-earth 0-diketonates in the visible, near ultra-violet and near infra-red is attributed to 4f-4f transitions. These transitions are electric dipole forbidden to first order, but are allowed by the electric quadrupole, vibronic, magnetic dipole and forced electric dipole mechanisms. The magnetic dipole character of the Dq F transition of the Eu + ion was demonstrated in 1939 by... 

In this case p (r) is the external force and (r) is the corresponding system response. Alternatively we may find it convenient to express the charge distribution in tenns of point moments (dipoles, quadrupoles, etc.) coupled to the coiTesponding local potential gradient tensors, for example, H will contain terms of the form fi V and g VV (b , where fi and Q are point dipoles and quadrupoles respectively. 

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. 

In his calculation of the induced dipole-dipole and dipole-quadrupole processes of energy transfer Kushida (17) made use of the Judd-Ofelt1) expression for the forced electric dipole transition probability in the rare earths incorporated in solids. 

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 ... 

The conunon characteristic of these weak forces is that they are due to nonoverlapping electronic clouds of their constituents. They differ in the important aspect of their directional character. The atom-atom van der Waals force is directed along the line of centers of the two atoms. The forces between molecules with anisotropic charge distributions induce a preferred orientation of the molecules toward one another. One can mimic the effect of these by distributing discrete charges (and dipoles, quadrupoles and,... 

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