Molecular dipole moment, definition

The dielectric constant of the vaccum c(j is included in the susceptibility definitions as SI units are used throughout this work. The analogous definition can be applied to the microscopic polarization p of a molecule with the molecular dipole moment jli and the polarizabilities a,/3, and y instead of the static polarization P (0) and the susceptibilities y-P. 

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. 

Whatever the validity of these formulae and the underlying cavity field theories it is very desirable that, before applying them, the definition and consistency of the macroscopic quantities as measured by different groups should be assessed. Much of the discussion in the literature deals directly with the final values of the hyperpolarizability presented in the various experimental papers. In calculating these values different versions of the above procedures may have been employed and, in particular, different values of the molecular dipole moment inserted into y to extract the y value. It is relatively easy to identify how the microscopic parameter has been obtained and which molecular convention is being used provided the identity of the macroscopic quantity is clearly established. The symbol, F), (and its derivative, (9F i/9H )o) is introduced here to denote provisionally a reported macroscopic nonlinearity before assessing its precise definition. The unprimed symbols are defined in accordance with eqn (4.16). The most troublesome ambiguity in the... 

The new polar symmetry allows for the existence of macroscopic polarization, large or small, depending on the magnitude of the strain and molecular dipole moments shown by small arrows. Due to the distortions, the densest packing of our pears and bananas results in some preferable ahgimient of molecular skeletons in such a way that molecular dipoles look more up than down. By definition, the dipole moment of the unit volume is electric polarization. These simple arguments brought R. Meyer to the brilliant idea of piezoelectric polarization [25] ... 

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. 

The next section in this chapter provides a brief comparison of the dipole moment (magnitude and direction) for a set of simple alcohols. Experimental gas phase dipole moments45 are compared to ab initio and as molecular mechanics computed values. It is important to note that the direction of the vector dipole used by chemists is defined differently in classical physics. In the former definition, the vector points from the positive to the negative direction, while the latter has the orientation reversed. 

It may be noted that simple MOPAC AMI calculations suggest that the dipole moment of NOBOW is oriented antiparallel to the molecular arrow. As indicated in Figure 8.25, this means that for an up field, the molecular arrows are pointing down. Given the definition of the sign of P in FLCs, this also means that domains of the ShiCaPa phase with positive chirality have negative ferroelectric polarization, and vice versa. 

Spectroscopists have always known certain phenomena that are caused by collisions. A well-known example of such a process is the pressure broadening of allowed spectral lines. Pressure broadened lines are, however, not normally considered to be collision-induced, certainly not to that extent to which a specific line intensity may be understood in terms of an individual atomic or molecular dipole transition moment. The definition of collisional induction as we use it here implies a dipole component that arises from the interaction of two or more atoms or molecules, leading at high enough gas density to discernible spectral line intensities in excess of the sum of the absorption of the atoms/molecules of the complex. In other... 

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 difference between the definitions of the shift operators J and the spherical tensor components T, (./) should be noted because it often causes confusion. Because J is a vector and because all vector operators transform in the same way under rotations, that is, according to equation (5.104) with k = 1, it follows that any cartesian vector V has spherical tensor components defined in the same way (see table 5.2). There is a one-to-one correspondence between the cartesian vector and the first-rank spherical tensor. Common examples of such quantities in molecular quantum mechanics are the position vector r and the electric dipole moment operator pe. 

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