Quadrupole-induced dipole

The presence of a field influences the wave function, and leads to induced dipole, quadrupole etc. moments. For the dipole moment this may be written as... 

For polarizable charge distributions, additional classical-type interactions arise from the induced dipole, quadrupole, and higher moments on each monomer, which are proportional to the fields created by the asymmetric charge distribution on the other monomer. The proportionality constants for each multipole field are the monomer polarizabilities aa and ah (a111 for dipole fields, a(Q) for quadrupole fields, etc.). The leading two induction interactions are ... 

A rotation of the H2 molecule through 180° creates an identical electric field. In other words, for every full rotation of a H2 molecule, the dipole induced in the collisional partner X oscillates twice through the full cycle. Quadrupole induced lines occur, therefore, at twice the (classical) rotation frequencies, or with selection rules J — J + 2, like rotational Raman lines of linear molecules. Orientational transitions (J — J AM 0) occur at zero frequency and make up the translational line. Besides multipole induction of the lowest-order multipole moments consistent with... 

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]... 

Method of moments. In rare gas mixtures, the induced dipole consists of just one B component, with Ai AL = 0001, Eq. 4.14. Alternatively, one particular B(c) component may cause the overwhelming part of a measured spectrum, like the quadrupole-induced component in mixtures of small amounts of H2 in highly polarizable rare gases ((c) = Ai AL = 2023, Eq. 4.59) in a given spectral range, other components (like 0001, 2021,...) are often relatively insignificant. In such cases, one can write down more or less discriminating relationships between certain spectral moments of low order n that are obtainable from measurements of the collision-induced spectral profile, g Al(o>),... 

H2 quadrupole moment, <72(re) at the fixed equilibrium position, and thus the long-range coefficient of the quadrupole-induced dipole component, Eq. 4.3, is about 5% too small relative to the proper vibrational average, <12 = (v = 0 < 2(r) f = 0) [216, 217, 209], A 5% difference of the dipole moment amounts to a 10% difference of the associated spectral intensities. Furthermore, the effects of electron correlation on this long-range coefficient can be estimated. Correlation increases the He polarizability by 5% but decreases the H2 quadrupole moment by 8% [275], a net change of-3% of the leading induction term B R). 

Table 4.12 shows that several of these correction coefficients are of nearly the same magnitude but of opposite sign, for example, for the = 2023 and 0223 components, (00 yl 01) and (00, 4 0T). Therefore, in Fig. 4.3 we need to give only one representative example of these functions. A similar situation exists for the four correction terms of the 2021,0221 components. The comparison of Figs. 4.2 (right-hand plot) and 4.3 shows that the correction terms belonging to the same /l AL set show very much the same dependence as the dipole coefficient for the rotationless case, i.e., the quadrupole induced terms reflect the R 4 dependence... 

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. 

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... 

Figure 6.14 compares the results of line shape computations based on the isotropic interaction approximation with the measurement by Hunt [187], This spectrum does not have many striking features because of the relatively high temperature of 300 K. We notice only a broad, unresolved Q branch and a diffuse Si(l) line of H2 is seen other lines such as Si(J) with J = 0, 2, 3,. .. are barely discernible. Various dips of the absorption at 4126, 4154 and 4712 cm-1 are caused by intercollisional interference, a many-body effect which is not accounted for in a binary theory. Roughly 90% of the Q branch (in the broad vicinity of 4150 cm-1) arises from the isotropic overlap induced dipole component (XL = 01). The anisotropic overlap component (XL = 21) is a little less than one-half as intense as the quadrupole induced term (XL = 23). These two components with X = 2 are responsible for the Si line structures superimposed on the broad isotropic induction component which is of roughly comparable intensity near the Si line center. 

Ternary spectral moments of collision-induced absorption in hydrogen gas are analyzed in the H2 fundamental band in terms of pairwise additive and irreducible contributions to the interaction-induced dipole moment, Eqs. (1 - 7) [51]. Numerical results show that irreducible dipole components, especially of the exchange quadrupole-induced ternary dipole component, are significant for agreement with spectroscopic measurements, such as ternary spectral moments (Fig. 1) [53], an observed diffuse triple transition 3<3i centered at 12,466 cm-1 [52, 54, 55], and the intercollisional dip in compressed hydrogen gas, pp. 188 -190. 

The intermolecular forces of adhesion and cohesion can be loosely classified into three categories quantum mechanical forces, pure electrostatic forces, and polarization forces. Quantum mechanical forces give rise both to covalent bonding and to the exchange interactions that balance tile attractive forces when matter is compressed to the point where outer electron orbits interpenetrate. Pure electrostatic interactions include Coulomb forces between charged ions, permanent dipoles, and quadrupoles. Polarization forces arise from the dipole moments induced in atoms and molecules by the electric fields of nearby charges and other permanent and induced dipoles. 

The quantity on the left is the Fourier component of the dipole moment induced by the optical field Max(w). These equations can be generalized to mixed frequency-dependent electric dipole, electric quadrupole, magnetic dipole properties, and similar equations can be written for the Fourier components of the permanent electric quadrupole, aj8(magnetic dipole, ma(co). For static Maxwell fields similar expansions yield effective (starred) properties, defined as derivatives of the electrostatic free energies. 

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 ... 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

The long-range potential is electrostatic. It comprises an isotropic van der Waals 0 R ) part, a dipole-induced dipole 0 R ) part, and a quadrupole-induced dipole 0 R ) part. 

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

Here the d are the analogs of the a in the expression for the induced dipole-dipole interaction and have been discussed by Margenau (89, 90). Ss and Ss are sums of the type l/(ri/ro) over all like and all unlike ions in the crystal lattice. They have been computed by Lennard-Jones and Ingham (8 ) for various lattice types and are given in Table IX. The actual value of the induced dipole-quadrupole term is about one tenth th t of the induced dipole-dipole term. 

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