Dipole electric field dependence

The response of solvent to an electrical field depends on the intrinsic dipole moment of its molecules, but depends also on cooperative effects of adjacent dipoles, when these are correlated in the Uquid. 

Electric field dependent electronic polarization in a molecule yields a field dependent dipole moment ... 

The polarizabilities are calculated from the electrical field dependence of either the total molecular energy or the dipole moment the y2 ]ki in crystals obey the laws of crystal symmetry and are measured using powerful laser sources. 

Effect of an electric field on a polar bond. A bond with a dipole moment (as in HF, for example) is either stretched or compressed by an electric field, depending on the direction of the field. Notice that the force on the positive charge ism the direction of the electric field (E), and the force on the negative charge is in the opposite direction. 

The parameter in Equation 8 is referred to as the orientation factor of FRET. This factor represents the angular dependence of the interaction energy between the acceptor transition dipole and the oscillating dipole electric field of the donor, is the source of much debate and many misunderstandings. It is the most difficult factor to control and usually the hardest to determine with confidence (28, 48). Therefore, we will spend more time discussing this factor. 

An alternative means for the experimental evaluation of //da is by means of electroabsorption spectroscopy. " The electric field dependence of the absorption spectrum can be used to obtain the difference in the ground state and excited state dipole moments, A/UdaI- This may be combined with the transition dipole moment (in Debyes), l gel = 16[Cda/(108 x 10 da)]. to obtain (neglecting vibronic and nonresonance overlap contributions), ... 

Thus, in general, the induced dipole moment will reach a saturation value m. As pictured in Figure 2, a restricted charge displacement may be accompanied by an orientational charge of the dipole axis. The electric field dependence of the total moment may be described in terms of coth functions as in the case of the counterion polarization in linear polyelectrolytes. See also Yoshioka et... 

The model outlined in Figure 1 for bacteriorhodopsin is suggestive not only for a possible control function of the electric field of the bacterial membrane during the photocycle of bacteriorhodopsin, but also for a possibly general, induced-dipole mechanism for electric-field-dependent... 

Dielectrophoresis (DEP) is a phenomenon different from electrophoresis (EP). In fact, any nonpolar material experiences a certain degree of polarization when exposed to an electric field. Depending on the material properties of the particle, electric dipoles are generated on opposing ends of the particle. The DEP force is due to the interaction between the dipole induced by an appfied electric field and the spatial gradient of that electric field. The general expression of the DEP force exerted on a particle in an electric field is... 

The expression (S2) is also a useful way to introduce a simplification suggested by Lazzeretti, which is that the dipole derivative can be obtained as the electric field dependence of the Hellmann-Feynman force. Buckingham and Fowler have pointed out that this approach is extendable to any multipole moment or polarizability derivative.In this case, all basis function derivatives drop out of the equations and the result is just... 

Here A02 = A20 and A22 are coupling coefficients that follow from the expressions derived above. Note that all these coefficients are functions of the electric field . Now, the comparison of dipolar and centrifugal energies defines another typical length scale for the interaction, namely, the one where = h /nirR, defining a dipole radius (More properly, one could define an electric-field-dependent... 

The intensity of an infrared absorption band is proportional to the square of the transition moment (or infrared active dipole moment). The absolute intensity of an infi ared band also depends upon the direction of the transition moment (dipole electric field vector) and the field direction vector (electric field vector) of the incident infrared radiation. The proportion of the transition moment (TMp) in the direction of the infrared electric field direction vector (E) is given as... 

Fig. 4.1 Systems of charges with no net charge but with either a dipole moment (A) or a quadmpole moment but no dipole moment (B). The origin of the coordinate system is the center of charge in each case. The energy of interaction of the system with a constant external electric field depends on the dipole moment, and so is zero in (B). The quadmpole moment becomes important if the magnitude of the external electric field (lf l) varies with position. The shaded backgrounds here represent a field that increases in strength with position in the X direction...

The electric field dependence of M, . and l/ , are reported in the top of Fig. 1.11, where they are plotted versus BOA. The shape and magnitude of the curve for linear polarizability versus BOA are well reproduced by the simple model. The two-state model" thus constitutes a good approximation to describe the F dependence of the linear polarizability in such donor-acceptor polyenes. Through this model, the evolution of a can be easily understood. The first transition energy evolves with the applied electric field in such a way that, as a function of BOA, l/ , ., peaks at the cyanine limit (Fig. 1.1 la). Furthermore, the transition dipole moment A/, between the ground state and 5 evolves in a similar way as a function of BOA (note that M., . is maximized at the cyanine limit since in that situation the and 5i wave functions are most similar). The product l/ , times M, /, which constitutes the aulmodel], then evolves, as a function of BOA, in such a way as to be maximized at the cyanine limit, where BOA = 0. 

Assuming that the system has no pennanent dipole moment, tire existence ofP(t) depends on a non-stationary j induced by an external electric field. For weak fields, we may expand the polarization in orders of the perturbation. 

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