Induced dipole moments

The dipole polarizability tensor characterizes the lowest-order dipole moment induced by a unifonu field. The a tensor is syimnetric and has no more than six independent components, less if tire molecule has some synnnetry. The scalar or mean dipole polarizability... 

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

The main difference between a molecule-molecule (M-M) collision and an ion-molecule (M+-M) collision is the presence of a polarization force in the latter system owing to the attraction between the static charge on M+ and the dipole moment induced on M. For a large inter molecular separation, the polarization energy is known as... 

The electric dipole moment induced in the system by the electric field is therefore... 

Interfacial dipole moment induced by contact adsorption... 

If electron clouds of cations and anions are deformable in an electric field and thus have polarizabilities of a+ and a, the value of the dipole moment induced in the cations by the presence of anions (p +) and induced in the anions by the presence of cations (p+ ) are, respectively, proportional to a+/P and a /r. The electric field acting on the cations is proportional to -a+]l L + /r, where 71I+ is the mean square dipole moment of the cations. 

Like the Coulombic forces, the van der Waals interactions decrease less rapidly with increasing distance than the repulsive forces. They include interactions that arise from the dipole moments induced by nearby charges and permanent dipoles, as well as interactions between instantaneous dipole moments, referred to as dispersion forces (Israelachvili 1992). Instantaneous dipole moments can be thought of as arising from the motions of the electrons. Even though the electron probability distribution of a spherical atom has its center of gravity at the nuclear position, at any very short instance the electron positions will generally not be centered on the nucleus. 

We noted in the preceding section that the polarizability of an ellipsoid is anisotropic the dipole moment induced by an applied uniform field is not, in general, parallel to that field. This anisotropy originates in the shape anisotropy of the ellipsoid. However, ellipsoids are not the only particles with an anisotropic polarizability in fact, all the expressions above for cross sections are valid regardless of the origin of the anisotropy provided that there exists a coordinate system in which the polarizability tensor is diagonal. 

A solution to the problem of scattering by an arbitrary particle could be obtained in principle by computing the dipole moment induced in each of its constituent atoms by the incident field and the combined fields of all the other atoms. But even a small particle (say 1 /xm) contains more than 1010 atoms. 

G. C. Pimentel (Berkeley) In discussing the excess dipole-moment induced by the formation of an H bond, Professor Coulson has noted that the necessary value of Z e9 the effective proton charge, is 2-3. I wonder if this is a rather high estimate of the necessary effective charge because the centre of gravity of the non-bonding electrons is closer to the proton than is the oxygen atom ... 

The dipole moment induced by the light wave is a transitory dipole moment and is not related to the permament dipole moment of the molecule. It is known as transition moment. 

Supermolecular spectra could perhaps be studied with state-selection using adequate molecular beam techniques. That would not be easy, however, because of the smallness of the dipole moments induced by in-termolecular interactions. For the purpose of this book, we will mostly deal with bulk spectra, or interaction-induced absorption of pure and mixed gases. A great variety of excellent measurements of such spectra exists for a broad range of temperatures, while state-selected supermolecular absorption beam data are virtually non-existent at this time. Furthermore, important applications in astrophysics, etc., are concerned precisely with the optical bulk properties of real gases and mixtures. 

In the preceding chapter, we have seen examples of absorption spectra, mostly of non-polar, dense gases. Such absorption arises from dipole moments which atoms or molecules do not possess, unless they are in interaction with other atoms or molecules. For the duration of the interaction, dipoles are induced that absorb and emit radiation. In this Chapter, we will consider the causes and properties of dipole moments induced by intermolecular interactions. 

The dipole moment induced in a molecule, or in a group of molecules, is a finite range function of the intermolecular separations, R, which falls off faster than R-3 for R —> oo. Van Kranendonk has argued that, therefore, it is possible to expand the above equation in a series of cluster functions [400, 402]. If ft( 1 n) designates the dipole moment induced in the cluster of molecules 1 n when these are present alone in the given volume V, cluster functions 1/(1 n) can be defined according to... 

The letter m represents the position coordinate Rm of atom m. Here, /i(l,l ) is the dipole moment induced in the dissimilar pair 1,1 in total isolation from other atoms, etc. The U functions have the cluster property of being zero unless all the molecules appearing in the argument are interacting at close enough range so that their spectral contributions are significant. The function U2 represents the dipole moment induced in the pair of... 

In this expression, 173 (123) is the dipole moment induced in a cluster of three like atoms and /i(12) == 0. 

It has been argued that, in the low-density limit, intercollisional interference results from correlations of the dipole moments induced in subsequent collisions (van Kranendonk 1980 Lewis 1980). Consequently, intercollisional interference takes place in times of the order of the mean time between collisions, x. According to what was just stated, intercollisional interference cannot be described in terms of a virial expansion. Nevertheless, in the low-density limit, one may argue that intercollisional interference may be modeled as a sequence of two two-body collisions in this approximation, any irreducible three-body contribution vanishes. 

In this expression, the s,s indicate the initial and final states of the supermolecule, Ps is the population probability of the state s, p is the dipole moment induced by intermolecular interactions, cosst = (Es — Es)/h where Es is the energy of the state s). For simplicity, we consider an atom-diatom system, such as H2-He, or a diatom-diatom system like H2-H2, with the absorption coefficient given by Eq. 6.50. Since we... 

Here, is the mean collision frequency of molecules of the type A with B vc(u) is the collision frequency of molecule A with A s initial speed being v P(v) is the probability density for AB collisions with A s initial speed being v K(v) is the intracollisional spectrum at zero frequency, per collision, with initial speed v A(v) is the mean projection of the integrated dipole moment induced by collisions with initial speeds v on the velocity... 

The dielectric properties of gases are closely related to collision-induced absorption. It is well known that collisions modify molecular properties. Specifically, we are here interested in the dipole moments induced by collisions (Chapter 4) which manifest themselves not only in collision-induced absorption, but also in the dielectric virial properties of gases. 

The dielectric constant e of a gas sample depends on the total dipole moment induced in response to an applied electric field. The dipole moment is the vector sum of the partially oriented permanent dipoles pt which individual molecules i may possess, plus the field-induced dipoles a, E arising from the polarizability a of the molecules i, plus all interaction-induced dipoles fiik, plus the field-induced dipoles which arise from the interaction-induced polarizability ptk [93]. The dielectric constant e depends, therefore, on the density g of the gas, according to... 

The comparison of Eqs. (1,2,3) shows that the ternary dipole functions B arising from the dipole moment induced in molecules 1,2 are related to the pair dipole functions B, according to... 

The pair dipole moment induced in molecules 1,3 may be similarly written,... 

M. Moraldi and L. Frommhold. Dipole moments induced in three... 

---