Dipole moment second-order

Here, f, Fx and are local field factors, a is a molecular parameter including the dipole moment, second order and third order hyperpolarizabilities. Under condition F = Fx = the formula does not agree with the experiment for 8CB. Indeed, it follows that rji should increase at the transition from the nematic to smectic A phase according to the increase in (F2) However, in the experiment, Fn markedly decreases. The similar temperature behavior was earlier observed for dielectric permittivity of 8CB. In the latter case the decrease in is due to the antiparallel correlation of molecular dipoles in the smectic A phase, which results in a decrease in the effective dipole moment /x Thus, the decrease... 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

The second procedure, several aspects of which are reviewed in this paper, consists of directly computing the asymptotic value by employing newly-developed polymeric techniques which take advantage of the one-dimensional periodicity of these systems. Since the polarizability is either the linear response of the dipole moment to the field or the negative of the second-order term in the perturbation expansion of the energy as a power series in the field, several schemes can be proposed for its evaluation. Section 3 points out that several of these schemes are inconsistent with band theory summarized in Section 2. In Section 4, we present the main points of the polymeric polarization propagator approaches we have developed, and in Section 5, we describe some of their characteristics in applications to prototype systems. 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

Without loss of generality y = y can be assumed. If the dipole moment can be assumed to be a linear function of coordinate within the spread of the frozen Gaussian wave packet, the matrix element (gy,q,p, Pjt(r) Y,q, p ) can be evaluated analytically. Since the integrand in Eq. (201) has distinct maxima usually, we can introduce the linearization approximation around these maxima. Namely, the Taylor expansion with respect to bqp = Qq — Qo and 8po = Po — Po is made, where qj, and pj, represent the maximum positions. The classical action >5qj, p , ( is expanded up to the second order, the final phase-space point (q, p,) to the first order, and the Herman-Kluk preexponential factor Cy pj to the zeroth order. This approximation is the same as the ceUularization procedure used in Ref. [18]. Under the above assumptions, various integrations in U/i(y, q, p ) can be carried out analytically and we have... 

Indeed, both expressions predict quadratic dependence of AA on the dipole moment of the solute. As in the previous example, it is of interest to test whether this prediction is correct. Such a test was carried out by calculating AA for a series of model solutes immersed in water at different distances from the water-hexane interface [11]. The solutes were constructed by scaling the atomic charges and, consequently, the dipole moment of a nearly spherical molecule, CH3F, by a parameter A, which varied between 0 and 1.2. The results at two positions - deep in the water phase and at the interface - are shown in Fig. 2.3. As can be seen from the linear dependence of A A on p2, the accuracy of the second-order perturbation theory... 

From a study of the microwave spectrum of 2-methylselenophene, the second-order Stark effect in the ground state was determined.11 The technique used was double radiofrequency-microwave resonance. For the identification by the double resonance method transitions of chiefly the A-state were chosen. From these observations the components of the dipole moment of 2-methylselenophene and the total dipole moment were determined. 

The first process is due to Schottky barriers [30], which are electrical dipole moments that form at the metal I molecule interfaces, as discussed above [34,40]. The second process arises if the electrically-active portion of the molecule is placed asymmetrically within the metal I molecule I metal sandwich. This geometry is common, because a long alkyl tail is often needed to make the molecule amphiphilic so that it will form well-ordered Langmuir-Blodgett monolayers [76-78]. 

Thus, in a study on the properties of dipole systems, most promise is shown by the representation of chain interactions, which, first, reflects the tendency toward ordering of dipole moments along the axes of chains with a small interchain to intrachain interaction ratio. Second, this type of representation makes it possible to use, with great accuracy, analytical equations summing the interactions of all the dipoles on the lattice. Third, there are grounds for the use of the generalized approximation of an interchain self-consistent field presented in Refs. 62 and 63 to describe the orientational phase transitions. 

It is necessary to calibrate the 14C time scale for greater dating accuracy. However, the second-order variations are at least as important as the first-order constancy of atmospheric 14C. For example, they provide a record of prehistoric solar variations, changes in the Earth s dipole moment and an insight into the fate of C02 from fossil fuel combustion. Improved techniques are needed that will enable the precise measurement of small cellulose samples from single tree rings. The tandem accelerator mass spectrometer (TAMS) may fill this need. 

For weak electric fields the magnitude of the induced polarization is linearly proportional with the amplitude of the electric field. Yet, when the field strength increases, the linear relationship no longer holds, and nonlinear terms have to be taken into account. In this case, the induced dipole moment and polarization can be expressed up to second order in the electric field as11... 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

The reorganization of the solvent molecules can be expressed through the change in the slow polarization. Consider a small volume element AC of the solvent in the vicinity of the reactant it has a dipole moment m = Ps AC caused by the slow polarization, and its energy of interaction with the external field Eex caused by the reacting ion is —Ps Eex AC = —Ps D AC/eo, since Eex = D/eo- We take the polarization Ps as the relevant outer-sphere coordinate, and require an expression for the contribution AU of the volume element to the potential energy of the system. In the harmonic approximation this must be a second-order polynomial in Ps, and the linear term is the interaction with the external field, so that the equilibrium values of Ps in the absence of a field vanishes ... 

Equation 24.14 provides an alternative definition of the electronic responses they are derivatives of the energy s relative to the field E. Note that the response of order n, the nth derivative of the response to the perturbation, is the n + 1th derivative of the energy relative to the same perturbation. Hence, the linear response a t is a second derivative of the energy. Because the potential (E) and the density (p) are uniquely related to each other, the field can be formulated as a function of the dipole moment p. The expansion of the field in function of p can be obtained from Equation 24.12 which can be easily inverted to give... 

Cooper and Dutta [216] found that Li/Al LDHs intercalated with 4-nitro-hippuric acid could exhibit second harmonic generation, which is a frequencydoubling nonlinear optical process. This is due to a perpendicular monolayer packing of the guest in the interlayer, resulting in an ordered arrangement of dipoles and hence bulk dipole moment in the soUd. 

In this expression, the Einstein convention of summation over repeated indices has been followed p0 is the permanent dipole moment, while al7, fiijk, and yiJkl are the tensorial elements of the linear polarizability, and the second- and third-order hyperpolarizabilities of the molecule, respectively. 

One requirement for second-order non-linearity in optical molecules is that they exhibit non-centrosymmetric symmetry, i.e. they must be dipolar in nature and all point in the same direction. Hence, materials suitable for electro-optical uses should have high figures for the multiplier where p is the dipole moment and P the molecular second order optical non-linearity parameter. ... 

Figure 5.31 Selected electro-optic chromophores with the products of their dipole moments and second order hyperpolarisabilities at 1.9 pm.

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