Induced Molecular Dipole Moments

The phenomenon of two-photon absorption (2 PA) can be presented as a process of simultaneous absorption of two photons under high intensity irradiation, resulting in one excited molecule [Ij. The investigations of 2PA previously undertaken are of great interest for a wide variety of emerging applications [3,36-42]. The nature of 2PA can be described based on the interaction of molecular electrons with an optical field. On a microscopic level the displacement of molecular electronic charge under the electric field, E, is related to the induced molecular dipole moment fi ... 

How can we relate these macroscopic quantities to the microscopic parameters of molecules such as polarizability or a dipole moment With some precautions, the polarization of an isotropic liquid may be found as a sum of the field induced molecular dipole moments whose number coincides with the amount of dipolar molecules in the unit volume = pNJM (p is mass density, A a is Avogadro number, M is molecular mass) ... 

In addition to permanent and induced molecular dipole moments, transition moments caused by charge cloud distortion during collisions have been discussed for gas phase systems (Kiss, Gush, and Welsh, 1959 van Kranendonk, 1958). It was found that this distortion moment contribution is small and decreases rapidly with temperature. In the case of gas phase Nj, the observed absorption intensity (Colpa and Ketelaar, 1958 Ketelaar and Rettschnick, 1964) could be wholly accounted for on the basis of the molecular quadrupole-induced mechanism. We do not consider the distortion moment further here. 

Finite-Field Method. This method relies on deriving the various terms in the power series for the static-induced molecular dipole moment in terms of derivatives with respect to the local field. Therefore, if the molecular dipole moment can be calculated as a fimction of local electric field E then is obtained from the second derivative of this fimction atE = 0. 

Since the parameters used in molecular mechanics contain all of the electronic interaction information to cause a molecule to behave in the way that it does, proper parameters are important for accurate results. MM3(2000), with the included calculation for induced dipole interactions, should model more accurately the polarization of bonds in molecules. Since the polarization of a molecular bond does not abruptly stop at the end of the bond, induced polarization models the pull of electrons throughout the molecule. This changes the calculation of the molecular dipole moment, by including more polarization within the molecule and allowing the effects of polarization to take place in multiple bonds. This should increase the accuracy with which MM3(2000) can reproduce the structures and energies of large molecules where polarization plays a role in structural conformation. 

Raman and IR spectroscopies are complementary to each other because of their different selection rules. Raman scattering occurs when the electric field of light induces a dipole moment by changing the polarizability of the molecules. In Raman spectroscopy the intensity of a band is linearly related to the concentration of the species. IR spectroscopy, on the other hand, requires an intrinsic dipole moment to exist for charge with molecular vibration. The concentration of the absorbing species is proportional to the logarithm of the ratio of the incident and transmitted intensities in the latter technique. 

These interactions (dipole-dipole, dd dipole-induced dipole, di and induced dipole-induced dipole, ii) are a function of dipole moment and polarizability. It has been shown that the dipole moment cannot always be replaced entirely by the use of electrical effect substituent constants as parameters ". This is because the dipole moment has no sign. Either an overall electron donor group or an overall electron acceptor group may have the same value of fi. It has also been shown that the bond moment rather than the molecular dipole moment is the parameter of choice. The dipole moments of MeX and PhX were taken as measures of the bond moments of substituents bonded to sp and sp hybridized carbon atoms, respectively, of a skeletal group. Application to substituents bonded to sp hybridized carbon atoms should require a set of dipole moments for substituted ethynes. 

Molecular crystals are among the most efficient second- and higher-harmonic generating materials. An external electric field E, upon interacting with a molecule, will induce a dipole moment p. If the field is strong, the response may not be linear, in which case the components of p can be developed in increasing powers of E as described by the expansion (i = 1, 2, 3)... 

The selection rules for the Raman spectrum turn out to depend not on the matrix elements of the electric dipole moment, but on the matrix elements of the molecular polarizability, which we now define. The application of an electric field E to a molecule gives rise to an induced electric dipole moment djnd (which is in addition to the permanent dipole moment d). If E= "> 1 + yl+ >zk, then the induced dipole moment has the components... 

From Fig. 9.1.1, it is clear that the polarization of the solvent will tend to enhance the electrical asymmetry of the molecule, i.e., enhance the molecular dipole moment. The resulting dipole moment p is then the permanent dipole plus an induced dipole moment ... 

By analogy with the the Onsager s theory, it is assumed that the response of the molecule to an external probing field can be expressed in terms of an external dipole moment fit, sum of the molecular dipole moment and the dipole moment arising from the molecule-induced dielectric polarization. Following ref. [8] and ref. [47],... 

The Raman effect can be seen, from a classical point of view, as the result of the modulation due to vibrational motions in the electric field-induced oscillating dipole moment. Such a modulation has the frequency of molecular vibrations, whereas the dipole moment oscillations have the frequency of the external electric field. Thus, the dynamic aspects of Raman scattering are to be described in terms of two time scales. One is connected to the vibrational motions of the nuclei, the other to the oscillation of the radiation electric field (which gives rise to oscillations in the solute electronic density). In the presence of a solvent medium, both the mentioned time scales give rise to nonequilibrium effects in the solvent response, being much faster than the time scale of the solvent inertial response. 

The principle behind this investigation is electrochromism or Stark-effect spectroscopy. The electronic transition energy of the adsorbed chromophore is perturbed by the electric field at the electric double layer. This is due to interactions of the molecular dipole moment, in the ground and excited states, with the interfacial electric field induced by the applied potential. The change in transition frequency Av, is related to the change in the interfacial electric field, AE, according to the following ... 

The polarity of a solid surface can be regarded as the strength of its average electrostatic field F. This field interacts with permanent or induced dipoles of adsorbed molecules, whereas its gradient interacts with permanent or induced quadrupoles. These interactions give rise to components of the adsorption energy such as EFfl (with permanent dipoles), Ef (polarization contribution) or PQ (with permanent quadrupoles). Therefore, the selection of the appropriate immersion systems, differing mainly in the molecular dipole moment n of the immersion liquid, can be expected to provide information on the value of EPfl since ... 

Molecular polarizability, a, is a measure of the ability of an external electric field, E, to induce a dipole moment, = aE, in the molecule. As such, it can be viewed as contributing to a model for induced dipole (dispersive) interactions in molecules. Because the polarizability is a tensor (matrix) quantity, there is the question of how to represent this in a scalar form. One approach is to use the average of the diagonal components of the polarizability matrix, (a x + otyy + Since the polarizability increases with size (and... 

The constant of proportionality a is called the polarisability of the molecule. For isotropic molecules, which include the monatomic molecules of the inert gases, the average direction of the induced molecular dipoles is in the direction of the applied field. (Since the local field is, as we shall see later, proportional to the overall applied field, we have m = const.E.) The total dipole moment per unit volume developed in this way, the polarisation P, is then related to the number of molecules per unit volume Nq . 

Figure 2.4-3 Molecular dipole moment induced by an electric field.

Polarizability of an Isolated Molecule.—In Cartesian tensor notation, the components of the molecular dipole moment p, induced by an electric field E, can be written as ... 

The effect of induced dipoles in the medium adds an extra term to the molecular Hamilton operator. = -r R (16.49) where r is the dipole moment operator (i.e. the position vector). R is proportional to the molecular dipole moment, with the proportional constant depending on the radius of the originally implemented for semi-empirical methods, but has recently also been used in connection with ab initio methods." Two other widely available method, the AMl-SMx and PM3-SMX models have atomic parameters for fitting the cavity/dispersion energy (eq. (16.43)), and are specifically parameterized in connection with AMI and PM3 (Section 3.10.2). The generalized Bom model has also been used in connection with force field methods in the Generalized Bom/Surface Area (GB/SA) model. In this case the Coulomb interactions between the partial charges (eq. (2.19)) are combined... 

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