Permanent dipole moment definition

For vapors, the local field vanishes because of the spherical symmetry and eqs A.5 and A.6 provide good agreement with experiment. However, for liquids one can no longer use eq A.6 for the polarizability in the Lorentz— Debye model. Indeed, for liquid water, eq A.5 diverges for values of y about 4 times smaller than the value of y for its vapor, which at 300 K is y = ye 4 yd = 32.3 x 10 40 C2 m2 J "1. One can regard eq A.5 as the definition of the molecular polarizability and calculate y in terms of the macroscopic dielectric constant e. The lower value of the polarizability in liquid than in vapor can be explained in the framework of the Lorentz—Debye model by the hindered rotation of the permanent dipole moment by the neighboring molecules in the condensed state. 

The conventional description of molecules, which is obviously much more intuitive and straightforward than its quantum-mechanical counterpart, is often adequate. Nevertheless, the manifestations of quantum effects are easily detectable experimentally. For example, species such as HfeCD, HD, or CH D, which are clearly nonpolar by the conventional definition, do possess temperature-dependent % and observable microwave spectra, and do deflect in inhomogeneous electric fields [11,16]. In fact, if one insists upon the conventional approach, these observations can be consistently accounted for by assuming the presence of small (of the order of 0.01 [D]) permanent dipole moments in these molecules. However, a rigorous quantum-mechanical treatment of such cases is clearly preferable. 

Owing to their definite structures, most biomolecules have an appreciable permanent dipole moment which must lead to dielectric polarization via the rotational mechanism of preferential orientation. Thus pertinent experimental investigation permits a direct determination of the molecular dipole moments and rotational relaxation times (or rotational diffusion coefficients, respectively). These are characteristic factors for many macro-molecules and give valuable information regarding structural properties such as length, shape, and mass. 

Van der Waals forces represent important intermolecular interactions between nonelectrolyte substances, and can be categorized into dipole-dipole, dipole-induced-dipole, and induced-dipole-induced-dipole forces. Polar molecules, by definition, will have a permanent dipole moment, and will interact with the oppositely charged portions or other molecules having permanent dipole moments. The dipole-dipole interaction is known as the orientation effect, or as the Keesom force. 

Polarity may be qualitatively defined as the ability of a solute to dissolve in a polar solvent, which results from interaction with surrounding molecules by dipolar, non-dispersive forces. By this definition, hydrocarbons are nonpolar because they possesses no permanent dipole moments, and the entire molecular surface must solely interact with its environment via dispersion forces. Thus methanol is more polar than octanol because the surface area of methanol that interacts only via dispersion forces (hydrophobic surface area) is much less than that of octanol. For liquids, increasing solute polarity generally causes an increase in water solubility. This is not necessarily true for solids because polarity... 

Following the discussion on ionic conductivity in section 12.1, and protonic conduction in section 12.1.2, it can definitely be seen that overall conduction in gum Arabica belongs to the aforementioned category. The nature of the mentioned conductivity is analyzed from a.c. conduction. In the microscopic level mechanism in the solid, there is a particular pair of states between which jumps take place which are influenced by the electric field. A dielectric material of natural type gum containing permanent dipole moment g, when sandwiched between two plane parallel electrodes of area A, separation d, the conductivity a and dielectric constant e are connected to conductance G and capacitance C by <7 = G (d/A) and = C (d/Eg A). In the absence of an external electric field, dipoles are oriented at random and possess only electronic polarizability in the field direction. 

By definition, molecules that are spherical tops do not have a permanent dipole moment, so they do not have a pure rotational spectrum. However, imder some conditions they may have rotational absorptions superimposed in their vibrational spectrum. 

When the MM subsystem is described through point charges and permanent dipole moments, the Hamiltonian (7) must be used and the Hartree-Fock equations are simply given by using the following Fock matrix definition ... 

When applied to solvents, this rather iU-defined term covers their overall solvation capabihly (solvation power) for solutes (i.e., in chemical equilibria reactants and products in reaction rates reactants and activated complex in light absorptions ions or molecules in the ground and excited state), which in turn depends on the action of aU possible, nonspecific and specific, intermolecular interactions between solute ions or molecules and solvent molecules, excluding such interactions leading to definite chemical alterations of the ions or molecules of the solute. Occasionally, the term solvent polarity is restricted to nonspecific solute/solvent interactions only (i.e., to van der Waals forces). With respect to this definition of polarity, when discussing dipolar molecules, the dipolarity (rather than polarity) of solvents should be considered. Molecules with a permanent dipole moment are dipolar (not polar). Molecules, which are lacking permanent dipole moment should be called apolar (or nonpolar). In literature, the terms polar and apo-lar are used indiscriminately to characterize a solvent by its relative permittivity as well as its permanent dipole moment, even though dipole moments and relative permittivities are not directly related to each other. 

Coordinate definitions, Lg and P matrices for H2O used in evaluating the atomic polar tensor elements are as given in section 3.3. With the aid of relation (4.14) die Pg matrix is transformed into vibrational polar tensor, while the rotational polar tensor is calculated using a permanent dipole moment value of-1.85 D [34]. The two submatrices obtained are as follows (in units of D A l) ... 

At the molecular level, electric quadrupoles can lead to useful structural information. Thus, whilst the absence of a permanent electric dipole in CO2 simply means that the molecule is linear, the fact that the electric quadrupole moment is negative shows that our simple chemical intuition of 0 C" 0 is correct. The definition of quadrupole moment is only independent of the coordinate origin when the charges sum to zero and when the electric dipole moment is zero. 

Linear Multipolar Electric Polarizabilities. Just as equation (40) served for defining the 2 -pole permanent electric moment, one can generalize the definition of the induced dipole (68) by introducing that of an induced 2 -pole moment. Assuming the inducing factor to be a uniform extamal electric field E, one has ... 

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric field. This arises because the centre of positive charge in the crystal does not coincide with the centre of negative charge. The phenomenon was discovered in 1920 by J. Valasek in Rochelle salt, which is the H-bonded hydrated d-taitrate NaKC4H406.4H20. In such compounds the dielectric constant can rise to enormous values of 10 or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various definitions and SI units ... 

The electric dipole-moment operator (14.14) is an odd function of the coordinates. If the wave function in (14.17) is either even or odd, then the integrand in (14.17) is an odd function, and the integral over all space vanishes. We conclude that the permanent electric dipole moment /u is zero for states of definite parity. 

These expansions serve mainly as definitions of the polarizabilities and hyperpolarizabilities as proportionality constants in the correction terms to the permanent moments. The dipole polarizability a is a second-rank tensor with nine cartesian components the dipole-quadrupole polarizability and first dipole... 

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