Rotation-induced dipole

The lower part shows a fluctuating field in phase with a rotating induced dipole, which is always directed with the field. 

Besides the collision-induced dipoles, we will occasionally refer to field-induced dipoles, or to rotation-induced dipoles, that is dipoles induced by an external electric field, or by centrifugal forces distorting certain symmetries of rotating molecules. Moreover, we will be interested in the dipoles induced in binary, ternary, etc., systems as we proceed. 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

Dielectric loss The dielectric loss factor represents energy that is lost to the insulator as a result of its being subjected to alternating current (AC) fields. The effect is caused by the rotation of dipoles in the plastic structure and by the displacement effects in the plastic chain caused by the electrical fields. The frictional effects cause energy absorption and the effect is analogous to the mechanical hysteresis effects except that the motion of the material is field induced instead of mechanically induced. 

Once again, the potential energy is inversely proportional to the sixth power of the separation. Notice that the potential energies of the dipole-dipole interaction of rotating polar molecules in the gas phase, the London interaction, and the dipole-induced-dipole interaction all have the form... 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

The induced dipole moment in a given direction fluctuates at double the rotational frequency of the molecule as shown schematically below. The upper diagram shows the electric field in phase with a rotating polar molecule. 

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

Molecules rotate. As a consequence, the induced dipole p(t) as function of time is likely to show a modulation by the rotational frequencies which, when Fourier transformed, leads to the appearance of induced rotational lines or bands. These occur at low frequencies in the microwave and far infrared region and are in general superimposed with the translational line, especially at higher temperatures. Only molecules that have a large rotational constant, e.g., H2 (Bo 60 cm-1), reveal substantial parts of the translational spectra, see Figs. 3.10 and 3.12, pp. 82 and 85, as examples. 

If molecular gases are considered, infrared spectra richer than those seen in the rare gases occur. Besides the translational spectra shown above, various rotational and rotovibrational spectral components may be expected even if the molecules are non-polar. Besides overlap, other induction mechanisms become important, most notably multipole-induced dipoles. Dipole components may be thought of as being modulated by the vibration and rotation of the interacting molecules so that induced supermolecular bands appear at the rotovibrational frequencies. In other words, besides the translational induced spectra studied above, we may expect rotational induced bands in the infrared (and rotovibrational and electronic bands at higher frequencies as this was suggested above, Eq. 1.7 and Fig. 1.3). Lines at sums and differences of such frequencies also occur and are common in the fundamental and overtone bands. We will discuss the rotational pair and triplet spectra first. 

An important induced dipole component of pairs involving molecules is multipolar induction. Specifically, the lowest-order multipole consistent with the symmetry of H2 is the electric quadrupole. Each H2 molecule may be thought of as being surrounded by an electric field of quadrupolar symmetry that rotates with the molecule.-In that field, a collisional partner X is polarized, thus giving rise to an induced dipole moment which in turn is capable of emitting and absorbing light. For like pairs, molecule 1 will induce a dipole in molecule 2 and 2 will induce one in 1. In... 

In conclusion, we note that for systems like HD-X, the intermolecular interactions become more anisotropic than for H2-X systems, because for HD the center of electronic charge and the center of mass do not coincide. The two centers differ by one sixth of the bond distance. Because the molecule rotates about the center of mass, new anisotropic terms appear in both the HD-X interaction potential and induced dipole components see Chapter 4 for details. 

An exception is the intercollisional dip which may be striking, especially in lines generated by isotropic overlap-induced dipoles rotational lines are less affected. 

Not all of these induced dipole types may exist in any given system. The components that exist generally couple in different ways to the translational, rotational, vibrational, etc., states of the complex and usually are associated with different selection rules, thus generating different parts of the collision-induced spectra. 

Here, the subscript (c) is short for the set of expansion parameters (c) = (2i, 22, A, L, oi, u2) r, is the vibrational coordinate of the molecule i R is the separation between the centers of mass of the molecules the Q, are the orientations (Euler angles a, jS y,) of molecule i Q specifies the direction of the separation / the C(2i22A M[M2Ma), etc., are Clebsch-Gordan coefficients the DxMt) are Wigner rotation matrices. The expansion coefficients A(C) = A2i22Al u1u2(ri,r2, R) are independent of the coordinate system these will be referred to as multipole-induced or overlap-induced dipole components - whichever the case may be. 

If no vibrational transitions are involved, for the purely rotational band, the rotation dependence is again quite weak and may safely be ignored for most purposes. Figure 4.2 (left-hand plot) shows the most significant induced dipole components for non-rotating molecules. 

HD-X induced dipoles. The HD molecule differs from H2 by its greater mass (which is of little concern here), the weak permanent dipole moment which arises from a non-adiabatic mechanism, and a center of mass which does not coincide with the center of electronic charge. Dipole moments are defined with respect to an origin that coincides with the center of mass. The presence of the permanent dipole leads to well-known rotational and rotvibrational spectra of RV(J) lines which show an interesting dispersion shape, arising from the interference of the induced and the allowed dipole spectra. For a theoretical analysis, one needs the induced dipole components of pairs like HD-X, with X = He, Ar, H2 or HD. These have been obtained previously [59] from the ab initio data for the familiar isotopes summarized above, using a simple coordinate transform familiar from potential studies of the isotopes. 

Hj-Ar-Ar rototranslational band. Experimental studies of the density variation of the rototranslational collision-induced absorption spectra of argon gas with a small admixture of hydrogen or deuterium have been reported [140, 108, 109, 106], Since there is no induced dipole component associated with Ar-Ar interactions, the spectroscopically dominant three-body interactions involve one hydrogen molecule and two argon atoms, H2-Ar-Ar. These spectra consist mainly of the quadrupole-induced rotational So(J) lines arising from the XL = 23 component. 

We have not attempted to exhibit in great detail the effects of the rotational excitations on the induced dipole components B and those of vibrational excitation on the interaction potential because this was done elsewhere for similar systems [151, 63,295,294], The significance of the j,f corrections is readily seen in the Tables and need not be displayed beyond that. The vibrational influence is displayed in Fig. 6.20 first and second spectral moments are strongly affected, especially at high temperatures, similar to that which was seen earlier for H2-He [294], Fig. 6.23. The close agreement of the measurements of the rotovibrational collision-induced absorption bands of hydrogen with the fundamental theory shown above certainly depends on proper accounting for the rotational dependences of the induced dipole moment, and of the vibrational dependences of the final translational states of the molecular pair. 

The computed profiles are shown in Figs. 6.11 and 6.12. The various components labeled XL = 01, 21, 23, and 45 are sketched lightly. Their sum is given by the heavy curve marked total. The spectra consist of a broad, purely translational part that is dominated at the low frequencies by the isotropic component (XL = 01). Other, generally smaller contributions are noticable, the most significant of which is the quadrupole-induced component (XL = 23) which shapes the rotational, induced lines, So(J) with J = 0,1,..., of H2 this component arises from a dipole component... 

The profiles of the rototranslational absorption of CH4-CH4 in the far infrared have been reported [56] see Fig. 3.22 for an example. The treatment of the spectra is based on the multipolar induction model and an advanced isotropic potential empirical overlap-induced dipole components have also been included for fitting the experimental data at several temperatures (126 through 300 K). At the lower temperatures, satisfactory fits of the measurements are possible. The analysis seems to suggest that at temperatures near room temperature a significant rotation-induced distortion of the tetrahedral frames occurs which affects the properties of the individual molecules (multipole strengths, molecular symmetry, polarizabilities, and perhaps the interaction). 

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