Dipole components

In principle, the distribution of ions and dipoles at the M/s interface is different from that at the free M and s surfaces. Therefore the Galvani potential may also be written, in the absence of specific adsorption, as the sum of the charge and dipole components ... 

Similar results were obtained with SrTiOj but not with CdS In the case of p-InP the opposite effect was found, i.e. an increase of the barrier height upon admittance of H2 to the metal. The nature of the ambient gas-induced changes were interpreted by a change in the surface dipole component of the metal work function . The results obtained with CdS did not fit into this scheme probably because the surfaw chemistry of this material is rather complex . ... 

The fact of a transfer of an electron from an absorbed particle to adsorbent [25] is widely considered as a criterion to differentiate between various forms of adsorption. Yet, as it has been already mentioned in previous section, there is a neutral form of chemisorption, i.e. weak binding formed without changing the surface charge state which only affects the dipole component of the work function. On the other hand, in several cases the physical adsorption can result in electron transitions in solids. Indeed, apart from formation of a double layer, changing the work function of adsorbent [26] the formation of surface dipoles accompanying physical adsorption can bring free charge carriers to substan-... 

As it has been already mentioned in numerous cases one should take into account the dipole component in the adsorption — caused change in the work function stemming from availability of dipole moment in adsorption particles. This component alters the value of micropotential of the surface. As it has been already mentioned in section 1.2, the origin of these dipoles can differ ranging from inherent to quantum mechanical one [4]. 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Although this procedure is based on solving a large number of equations, we have good confidence in the obtained results. For example, we found no good solutions if any of the components indicated with an asterisk was assumed to vanish. Further confidence in the results is provided by their excellent agreement with expected results. For example, we observe the common result that the electric dipole components y". - and yj are approximately equal, whereas is somewhat larger.38 39... 

Binary and ternary spectra. We will be concerned mainly with absorption of electromagnetic radiation by binary complexes of inert atoms and/or simple molecules. For such systems, high-quality measurements of collision-induced spectra exist, which will be reviewed in Chapter 3. Furthermore, a rigorous, theoretical description of binary systems and spectra is possible which lends itself readily to numerical calculations, Chapters 5 and 6. Measurements of binary spectra may be directly compared with the fundamental theory. Interesting experimental and theoretical studies of various aspects of ternary spectra are also possible. These are aimed, for example, at a distinction of the fairly well understood pairwise-additive dipole components and the less well understood irreducible three-body induced components. Induced spectra of bigger complexes, and of reactive systems, are also of interest and will be considered to some limited extent below. 

With this notation, the electric charge qo of a monopole equals Qoo-Cartesian dipole components px, py, pz, are related to the spherical tensor components as Ql0 = pz, Qi i = +(px ipy)/y/2, with i designating the imaginary unit. Similar relationships between Cartesian and spherical tensor components can be specified for the higher multipole moments (Gray and Gubbins 1984). 

Spectroscopists have always known certain phenomena that are caused by collisions. A well-known example of such a process is the pressure broadening of allowed spectral lines. Pressure broadened lines are, however, not normally considered to be collision-induced, certainly not to that extent to which a specific line intensity may be understood in terms of an individual atomic or molecular dipole transition moment. The definition of collisional induction as we use it here implies a dipole component that arises from the interaction of two or more atoms or molecules, leading at high enough gas density to discernible spectral line intensities in excess of the sum of the absorption of the atoms/molecules of the complex. In other... 

Theoretical estimates of the three-body moments may be obtained from the well-known pair dipole moments. These do not include the irreducible three-body components which are poorly known. Interestingly, in every case considered to date, the computations of the three-body spectral moments y[3 are always smaller than the measurements, a fact that suggests significant positive irreducible three-body dipole components for all systems hitherto considered [296, 299] further details may be found in Chapter 5. 

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. 

Fig. 3.24. Absorption coefficient, . v)/qiq2, of He-CH4 at 150 K. The measurements [3] are given as dots ( ) the heavy curve represents a fit of the three overlap components an isotropic dipole component (A = 0, dashed) and overlap components of octopolar and hexadecapolar symmetry (A = 3 and 4 dotted and dash-dotted, respectively) after [387].

It has been known since the early days of collision-induced absorption that spectral moments may be represented in the form of a virial expansion, with the coefficients of the Nth power of density, qn, representing the N-body contributions [402, 400], The coefficients of qn for N = 2 and 3 have been expressed in terms of the induced dipole and interaction potential surfaces. The measurement of the variation of spectral moments with density is, therefore, of interest for the two-body, three-body, etc., induced dipole components. 

For easy reference we also plot theoretical three-body moments of H2-H2-H2 which are computed from first principles based on the assumption of a pairwise-additivity, Figs. 3.46 and 6.2 (heavy curves). The pair dipole moments have been shown to allow a close reproduction of measured binary spectra from first principles in the hydrogen fundamental band, for temperatures from 20 to 300 K these are believed to be reliable. Interestingly, the pairwise-additive assumption is not sufficient to reproduce the experimental three-body moments from theory, except perhaps at the lowest temperatures. With increasing temperature, rapidly increasing differences between measured and computed moments are observed, a fact which suggests the presence of an irreducible three-body dipole component of the overlap-induced type [296]. 

Spectral moments of allowed molecular absorption bands vary in general nearly linearly with the gas density, y /q constant. At sufficiently high pressures, a small, linear increase with density of the ratio y /g is, however, discernible, e.g., [8]. This quadratic absorption component is largely due to apparent induced absorption, resulting from the long range interaction of dipoles induced by the incident radiation field [400], Moreover, a true induced absorption component is believed to exist which arises from collision-induced dipole components (Chapter 4) [146, 210]. It was argued, however, that in most measurements true induced absorption was too weak to be identified positively in this way. Recent experimental and... 

If at least one of the interacting particles is a molecule, further induction mechanisms arise. Molecules are surrounded by an electric field which may be viewed as a superposition of multipole fields. A collisional partner will be polarized in the multipole field and thus give rise to induced dipole components. In the case of symmetric diatoms like H2 or N2, the lowest-order multipole is a quadrupole and asymptotically, for R - 00, the quadrupole-induced dipole may be written as [288, 289]... 

Here a designates the trace of the polarizability tensor of one molecule (l/47i o) times the factor of a represents the electric fieldstrength of the quadrupole moment q2. Other non-vanishing multipole moments, for example, octopoles (e.g., of tetrahedral molecules), hexadecapoles (of linear molecules), etc., will similarly interact with the trace or anisotropy of the polarizability of the collisional partner and give rise to further multipole-induced dipole components. 

On a scale of the order of atomic size, molecular multipole fields vary strongly with orientation and separation. As a consequence, one will generally find induced dipole components arising from field gradients of first and higher order which interact with the so-called dipole-multipole polarizability tensor components, such as the A and E tensors. 

Here, the pt are the permanent dipoles of molecules i = 1 and 2, and the ptj( r, i 2, Rij) are the dipoles induced by molecule i in molecule j the are the vectors pointing from the center of molecule i to the center of molecule j and the r, are the (intramolecular) vibrational coordinates. In general, these dipoles are given in the adiabatic approximation where electronic and nuclear wavefunctions appear as factors of the total wavefunction, 0(rf r) ( ). Dipole operators pop are defined as usual so that their expectation values shown above can be computed from the wavefunctions. For the induced dipole component, the dipole operator is defined with respect to the center of mass of the pair so that the induced dipole moments py do not depend on the center of mass coordinates. For bigger systems the total dipole moment may be expressed in the form of a simple generalization of Eq. 4.4. In general, the molecules will be assumed to be in a electronic ground state which is chemically inert. 

For example, the permanent dipole components of a diatomic system may thus be written... 

In order for the induced dipole moment, ft, to transform as a vector, the spherical harmonics describing the various orientations have to be coupled in an appropriate way. We write the induced dipole components of a system of two molecules of arbitrary symmetry, according to [141]... 

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. 

Multipolar induction. For the description of the long-range dipole components, we start with the electric potential at the distance R outside the molecule 1 [323, 391]. In a space-fixed coordinate system, the potential is given as... 

The induced dipole component arising from the anisotropy yS( ) (ri) 0f the polarizability tensor is similarly obtained... 

While exchange- and dispersion-induced dipole components are of a quantum nature, the multipole-induced dipole components can be modeled by classical relationships, if the quantum effects are small. For many systems of practical interest, multipolar induction generates the dominant dipole components. The classical multipole induction approximation has been very successful, except for the weakly polarizable partners (e.g., He atoms) [193]. It models the dipole induced in the collisional partner by polarization in the molecular multipole fields. 

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