Dipole moment, average induced

In addition to the pear-shaped molecules, bent-shaped molecules were used to illustrate the dipolar origin of the flexoelectric effects in nematic liquid crystals. It was assumed that the constituent molecules of the nematic liquid crystals are free to rotate around their axes, and in the absence of electric fields, their dipole moments average out so the net polarization of the material is zero. However, when liquid crystals made from polar pear- or banana-shaped molecules are subjected to splay or bend deformations, respectively, they can become macroscopically polar, because the polar structures correspond to a more efficient packing of the molecules. It follows from symmetry considerations that the deformation-induced fiexo-electric polarization Pa can be written as ... 

The anisometry of mesogenic molecules leads to anisotropic polarization in electric fields. If an electric field, E, is applied to a molecule, a dipole moment is induced. The dipole tends to orient in the direction of the field. The average dipole moment per unit volume defines the polarization, P, which is proportional to the electric field ... 

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

Measurements of Stark splittings in microwave and radiofrequency spectra allow tliese components to be detennined. The main contribution to tire dipole moment of tire complex arises from tire pennanent dipole moment vectors of tire monomers, which project along tire axes of tire complex according to simple trigonometry (cosines). Thus, measurements of tire dipole moment convey infonnation about tire orientation of tire monomers in tire complex. It is of course necessary to take account of effects due to induced dipole moments and to consider whetlier tire effects of vibrational averaging are important. 

The actual evaluations of Edd, II, and EHH are complex. Note that for Edd, CKJ uses Buckingham s (1957) prescription for the number of dipoles in the first solvation shell and considers both the thermally averaged dipole moment and the induced moment. The polarization energy is obtained from Land and O Reilly (1967). 

London-van der Waals forces generally are multipole (dipole-dipole or dipole-induced dipole) interactions produced by a correlation between fluctuating induced multipole (principal dipole) moments in two nearly uncharged polar molecules. Even though the time-averaged, induced multipole in each molecule is zero, the correlation between the two induced moments does not average to zero. As a result an attractive interaction between the two is produced at very small molecular distances. 

A second type of force between water molecules and the metal consists of the dispersion forces. Dispersion forces (or London forces) can be seen classically as follows A time-averaged picture of any atom shows spherical symmetry because the charge due to the electrons orbiting around the nucleus is smoothed out in time. An instantaneous picture of, say, a hydrogen atom, would, however, show a proton here and an electron there—two charges separated by a distance. Hence, every atom has an instantaneous dipole moment of course, the time average of all these dipole moments is zero. This instantaneous dipole will induce an instantaneous dipole in a contiguous atom, and an instantaneous dipole-dipole force will arise. When these... 

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 . 

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). 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

For classical line shape calculations one needs the induced dipole moment as function of time, p(R(t)), averaged over angular momenta and speeds of relative motion. In other words, one solves Newton s equation of motion, or one of its integrals, of the two-particle system. After suitable averaging, one obtains the spectral profile by Fourier transform. 

Dispersion Interactions. Last but not least in the range of solute-solvent electrostatic interactions come the dispersion forces which depend on the polarizabilities of the molecules. Any atom or molecule—non-polar or polar—has a small fluctuating dipole moment as the electrons move around the nuclei. These instantaneous dipoles induce dipole moments in all other polarizable molecules, so that the interaction energy is proportional to the product of the average polarizabilities aM and as of the solute and solvent molecules... 

J. Gao, F. J. Luque and M. Orozco, Induced dipole moment and atomic charges based on average electrostatic potentials in aqueous solution, J. Chem. Phys., 98 (1993) 2975-2982. 

Table 3-8. Average solvent-induced dipole moments in the N, Z and V states for 81° twist angle...

Polarizability (of a molecule) — There are numerous different mechanisms that contribute to the total polarizability of a molecule. The three most important of these are termed electron polarizability, molecular-distortion polarizability, and orientation polarizability. All these parameters are measured as statistical averages over large numbers of molecules present in the bulk phase. (1) -> Electron polarizability a is a measure of the ease with which electrons tend to be displaced from their zero-field positions by the applied -> electric field. Thus, the electron polarizability of a molecule is defined as the ratio of induced dipole moment pincj (coulomb meters) to the inducing electric field E (volts per meter) ... 

Here ey is the cross section for a collisionally induced transition and v is the thermal velocity of the colliding particle, < av > is the average value of ov for a Maxwellian velocity distribution. Assuming a typical dipole moment of 1 Debye, a = 1CT15 cm"2, v = 5 x 104 cm/s, one obtains the density n % 103/X3. Thus for the detection of an emission line in the centimeter-wave region (X = 1 cm) the density within the cloud is expected to be of the order of 103 cm-3. On the other hand, a detection of a millimeter-wave transition in emission at X = 1 mm requires densities of the order of 10s to 106 particles/cm3. 

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