Moment, electric permanent

The polarization of the material in an electric field is consequent upon the development of an electric moment M in the material due to charge displacement under the field. Removal of the field results in the decay of M(t) which can be described in terms of a decay function (r) or as an ensemble averaged decay of the instantaneous electric moments (permanent plus induced), m(r) ... 

Under the influence of an electric field a gas whose molecules have a permanent electric moment and in addition can have a further moment induced in them by deformation becomes polarized in the direction of the field, the amount of polarization per unit volume being1... 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

One of the more profound manifestations of quantum mechanics is that this curve does not accurately describe reality. Instead, because the motions of electrons are correlated (more properly, the electronic wave functions are correlated), the two atoms simultaneously develop electrical moments that are oriented so as to be mutually attractive. The force associated with tills interaction is referred to variously as dispersion , the London force, or the attractive van der Waals force. In the absence of a permanent charge, the strongest such interaction is a dipole-dipole interaction, usually referred to as an induced dipole-induced dipole interaction, since the moments in question are not permanent. Such an interaction has an inverse sixtli power dependence on the distance between the two atoms. Thus, the potential energy becomes increasingly negative as the two noble gas atoms approach one another from infinity. 

Dispersion is a fascinating phenomenon. It is sufficiently strong that even tlie dimer of He is found to have one bound vibrational state (Luo et al. 1993 witli a vibrationally averaged bond length of 55 A it is a remarkable member of the molecular bestiary). Even for molecules with fairly large permanent electric moments in the gas phase, dispersion is the dominant force favoring condensation to the liquid state at favorable temperatures and pressures (Reichardt 1990). 

Our discussion of non-bonded interactions began with the example of two noble gas atoms having no permanent electrical moments. We now turn to a consideration of non-bonded interactions between atoms, bonds, or groups characterized by non-zero local electrical moments. 

Consider the case of two molecules A and B interacting at a reasonably large distance, each characterized by classical, non-polarizable, permanent electric moments. Classical electrostatics asserts the energy of interaction for the system to be... 

Analogous quantities to die electric moments can be defined when the external perturbation takes the form of a magnetic field. In this instance die first derivative defines the permanent magnetic moment (always zero for non-degenerate electronic states), the second derivative the magnetizability or magnetic susceptibility, etc. 

Equilibrium electrostatic interactions between a solute and a solvent are always nonpositive - tliey are zero if the solute is characterized by no electrical moments (e.g., a noble gas atom) and negative otherwise, i.e., attractive. It is easiest to visualize the electrostatic interactions as developing in a stepwise fashion. Consider a solute A characterized by electrical moments for simplicity, consider only die dipole moment. When A passes from the gas phase into a solvent, the solvent molecules, if diey have permanent moments of their own, reorient so that, averaged over thermal fluctuations, their own dipole moments oppose that of the solute. In an isotropic liquid with solvent molecules undergoing random thermal motion, the average electric field at any point will be zero however, the net orientation induced by the solute changes this, and the lield induced by introduction of the solute is sometimes called the reaction field . 

The adsorption of gas molecules on the interior surfaces of zeolite voids is an ionic interaction with a characteristic potential energy called the heat of adsorption. The molecular adsorption process results in an exothermic attachment of the gas molecules to the surface of the voids, and is characterized by a high order of specificity. Zeolites exhibit a high affinity for certain gases or vapors. Because of their "effective" anionic frameworks and mobile cations, the physical bonds for adsorbed molecules having permanent electric moments (N2, NH-j, H20) are much enhanced compared with nonpolar molecules such as argon or methane. 

In general, two types of adsorption are distinguished, physical adsorption and chemisorption, which depend on the type of interaction established between the adsorbent and the adsorptive. In a chemisorption process, specific chemical interactions between the adsorbent and the adsorptive occur, and the process is not reversible. On the other hand, physical adsorption includes attractive dispersion forces and, at very short distances, repulsive forces, as well as contribution from polarization and electrostatic forces between permanent electrical moments and the electrical field of the solid, if the adsorptive or the adsorbent has a polar nature. In this case, the process is fully reversible (or almost reversible). Thus, the overall interaction energy ( >(z) of a molecule of adsorptive at a distance z from the surface of the adsorbent is given by the general expression... 

Although the change in the quadrupole moment of OH expressed by equation (123d) (the first nonzero permanent electric moment is always independent of the choice of origin21 ) was not taken into account in building up the H02 DMBE potential of ref. 141, it is likely that the associated error will have no practical significance. 

These very weak forces arise by virtue of the polarization of a molecule by the charge or permanent electric moment on an adjacent molecule. In addition, polar bonds may result in bonds between atoms of greatly different electronegativity in which the shared pair of electrons are distorted from a symmetrical distribution. These induction forces, though of low energy, are of some import in the binding of lipids and proteins. 

Influence of a Permanent Electric Moment on the Heat of Adsorption of a Gas or Vapor... 

So far in this discussion, the contribution of an electric moment interaction with an ionic field has been neglected. This is justifiable on the basis of the observed results, but Kington and Macleod (11) recently found a correlation between a heat of adsorption term and the permanent quadrupole moment of the gas involved, and from this correlation they concluded that a major part of the energy heterogeneity in adsorption may be laid to the interaction between the quadrupole and the position-dependent field gradient in the solid. It is therefore necessary to examine this idea in the present context. 

In this equation, N is the number of molecules per cubic centimeter, T is absolute temperature, p is the permanent electrical moment, and a is a constant. 

Table 8 Natural permanent) multipole electric moments of simple molecules...

Linear Multipolar Electric Polarizabilities. Just as equation (40) served for defining the 2 -pole permanent electric moment, one can generalize the definition of the induced dipole (68) by introducing that of an induced 2 -pole moment. Assuming the inducing factor to be a uniform extamal electric field E, one has ... 

For tetrahedral molecules the linear polarizability is isotropic, and the first non-zero permanent electric moment is the octupole Q = TlJe electric fields of these octupoles induce a dipole moment in any given molecule, whence 0 and we have by equation (241) to a suflBciently good approximation ... 

Dispersional Interaction between Molecules. We still wish to consider briefly energies due to interaction between fluctuating induced electric charge distributions of atoms and molecules. In constrast to electrostatic and induced interactions, these are present even when the molecules do not possess permanent electric moments. These dispersional interactions cannot be dealt with on a classical electrostatics level owing to their relation to London s quantum dispersion theory, they have been termed London dispersional interactions. 

Quadratic Permittivity Variations in Gases and Liquids. -Gases and Dilute Dipolar Media. We shall calculate Ae within the framework of the classical Langevin-Debye theory. The total electric moment of a dipolar molecule having the permanent electric moment p and linear electric polarizability a immersed in a field E is ... 

These results having been obtained, the method was used to investigate a problem of fundamental importance in the realm of chemical constitution. According to Weissenberg s theory, substances of the type Ca, i.e. methane derivatives with all four substituents the same, should not only be able to exist in the form of a regular tetrahedron, but there should also exist molecular forms in which the C-atom is situated at the vertex of a pyramid and the four substituents at the four corners of the base. Molecules with the first type of structure should have no electric moment, whereas those with the second type should exhibit a permanent dipole moment. Pentaerythritol, C(CH20H)4, is frequently quoted as an example of the second type of structure. The moment of this substance cannot be found by the dielectric-constant method, as it... 

The "stickiness shown by water is not found in small molecules without permanent electric moments. Their mobility within crystals is governed much more by the openness of the frameworks, modified by the siting of the cations, which may partially obscure the window apertures. 

Al content (4). These results all exemplify how framework charge density affects heats of sorption of molecules possessing permanent electric moments. 

Figures 5.7 and 5.8 sketch a picture of the first two permanent electric moments (au) for a selection of noncentrosymmetric and centrosymmetric molecules, respectively. The notation is the same as that given in Mag-nasco et al. (1988). It is understood that the point-like multipoles are placed at the centre of mass of the molecule, their sign in relation to the molecular structure of the monomer being of fundamental importance in determining the nature of the electrostatic interaction (attractive or repulsive). The numbers shown in each figure are from SCF calculations and so are little larger than those given in Table 5.2.

Figure 5.7 The first two permanent electric moments of some noncentrosymmetric molecules...

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