Field strength, dipole moment

Two polarization mechanisms are possible. If the molecules possess a permanent electric dipole moment pbp rm, each molecule can align its moment with the field direction by reorientation, producing a macroscopic dipole moment. Even if perm = 0 in the field-free limit, each molecule can achieve a field-dependent dipole moment pind by induction. The induced dipole moment is proportional to field strength, pind = a , where a is the electric polarizability of the molecule. In both cases, work must be performed on the system to achieve the macroscopic polarization. Molecules with large permanent dipole moments correspond to high k. 

If a material of polar molecules, such as water, is exposed to a fixed or static electric field, the molecules will all rotate in an attempt to orient themselves in the direction of the field. The magnitude of separated charges of a polar molecule is defined as the dipole moment, and determines the strength of interaction with the field. The dipole moment is also a measure of the dielectric constant e. A symmetrical molecule, with no dipole moment, is said to be non-polar and does not react with an electric field. If an electric field impinging upon a polar molecule is alternating, the molecules will rotate, following reversals of field. 

Generally, field strengths from 0.0001 au up to 0.0128 au were tried in the Eckart-constrained optimizations and the energies and dipole moments of the successfully optimized structures were subjected to a numerical Romberg differentiation. As in the case of the electronic properties, the numerical differentiation of the energies was too unstable to yield aU the properties of interest. However, the numerical differentiation of field-induced dipole moments allowed us to obtain stable values for most of the components of the NR contribution to the static a, / and 7 and to the lOF approximation for the dc-Pockels first hyperpolarizabiUty. Due to the high computational cost of these calculations, the 6-3IG basis set had to be used. A few control calculations with the 6-31-hG basis set showed that the influence of diffuse basis functions on the vibrational properties is not negligible, but smaller than on the electronic properties. 

The af i (Ml) term thus deseribes the interaetion of the magnetie dipole moments of the eleetrons and nuelei with the magnetie field (of strength H = Aq k) of the light (whieh lies along the y axis) ... 

Now let us examine the molecular origin of Molecular polarity may be the result of either a permanent dipole moment p or an induced dipole moment ind here the latter arises from the distortion of the charge distribution in a molecule due to an electric field. We saw in Chap. 8 that each of these types of polarity are sources of intermolecular attraction. In the present discussion we assume that no permanent dipoles are present and note that the induced dipole moment is proportional to the net field strength at the molecule ... 

The magnitude of the induced dipole moment depends on the electric field strength in accord with the relationship = nT, where ]1 is the induced dipole moment, F is the electric field strength, and the constant a is caHed the polarizabHity of the molecule. The polarizabHity is related to the dielectric constant of the substance. Group-contribution methods (2) can be used to estimate the polarizabHity from knowledge of the number of each type of bond within the molecule, eg, the polarizabHity of an unsaturated bond is greater than that of a saturated bond. 

Thus the kinetic equation may be derived for operator (7.21), though it does not exist for an average dipole moment. Formally, the equation is quite identical to the homogeneous differential equation of the impact theory with the collisional operator (7.27). It is of importance that this equation holds for collisions of arbitrary strength, i.e. at any angle of the field reorientation. From Eq. (7.10) and Eq. (7.20) it is clear that the shape of the IR spectrum... 

The double layer is described by its effective thickness, d, and by its field strength E (Fig. 6.15). The adsorbed moleculeJias a dipole moment P. It is well documented100 that the local field strength E can affect strongly not only the chemisorptive bond strength but also the preferred orientation of the adsorbate (Fig. 6.16). 

Many of the initial theoretical models used to vahdate the concept of coherent control and optimal control have been based on the interaction of the electric field of the laser light with a molecular dipole moment [43, 60, 105]. This represents just the first, or lowest, term in the expression for the interaction of an electric field with a molecule. Many of the successful optimal control experiments have used electric fields that are capable of ionizing the molecules and involve the use of electric field strengths that lead to major distortions of the molecular electronic structure. With this in mind, there has been discussion in the... 

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... 

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

If quark matter is in the ferromagnetic phase, it may produce the dipolar magnetic field by their magnetic moment. Since the total magnetic dipole moment Mq should be simply given as Mq = fjq (47t/3 rq)nq for the quark sphere with the quark core radius rq and the quark number density nq. Then the dipolar magnetic field at the star surface R takes the maximal strength at the poles,... 

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