Electric dipole moments, permanent

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric held. 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-tartrate NaKC4H406.4H 0. In such compounds the dielectric constant can rise to enormous values of lO or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various dehnitions and SI units ... 

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. 

Breakdown of the Bom-Oppenheimer approximation is responsible for the small but non-zero permanent electric dipole moment of HD (2 x 10 Cm, Trefler and Gush, 1968) but otherwise the effect is negligible to chemical accuracy. 

Here, auir) is the mean polarizability of a pair of species separated by distance r, while pn is their electric dipole moment and U the potential energy, p o is the permanent electric dipole moment for the two species at infinity. 

Besides these response properties of a molecule we will also devote one section in this chapter to the experimentally important infrared intensities, which are needed to complement the theoretically predicted frequencies for the complete computational simulation of an IR spectrum. This discussion belongs in the present chapter because the infrared intensities are related to the derivative of the permanent electric dipole moment p with respect to geometrical parameters. 

Born-Oppenheimer approximation, permanent electric dipole moment, 246—249... 

Standar model (SM), particle physics, electron electric dipole moment, 242-243 Stark effect, permanent electric dipole moment, 245-249... 

Usually we call neutral molecule as polar one if it has considerable permanent electric dipole moment /i°. The total dipole moment should include also an induced one, aR (a is a polarizability of the molecule, R is the intensity of electric field interacting with molecule), and may be presen ted as /i = /<° + a . Permanent part of dipole moment for nonsymmetrical organic molecules usually accepted to be essentially larger than induced one that is why orientational forces or interactions of permanent electric dipoles are the most important in polar solutions [1,2,4,12, 39]. 

Rotational spectra are due to charges that occur on molecules with permanent electric dipole moments. As the molecule rotates the dipole moment... 

An interaction, either intermolecular or intramolecular, between molecules, groups, or bonds having a permanent electric dipole moment. The distance and relative orientation between the two dipoles governs the strength of this interaction. See also van der Waals Forces... 

LiH is the simplest uncharged molecule that has a permanent electric dipole moment. We examine here some of the properties of the simplest VB functions for this molecule. The molecule is oriented along the z-axis with the Li atom in the positive direction. 

After discovery of the combined charge and space parity violation, or CP-violation, in iT°-meson decay [7], the search for the electric dipole moments (EDMs) of elementary particles has become one of the most fundamental problems in physics [6, 8, 9, 10, 1]. A permanent EDM is induced by the weak interaction that breaks both the space symmetry inversion and time-reversal invariance [11]. Considerable experimental effort has been invested in probing for atomic EDMs induced by EDMs of the proton, neutron and electron, and by P,T-odd interactions between them. The best available restriction for the electron EDM, de, was obtained in the atomic T1 experiment [12], which established an upper limit of de < 1.6 X 10 e-cm, where e is the charge of the electron. The benchmark upper limit on a nuclear EDM is obtained in atomic experiment on i99Hg [13], ]dHgl < 2.1 X 10 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 " e-cm, was also recently obtained by Dmitriev Sen kov [14] (the previous upper limit on the proton EDM was obtained in the TIE experiment, see below). 

Orientation polarization can occur in materials composed of molecules that have permanent electric dipole moments. The permanent dipoles tend to become aligned with the apphed electric field, but entropy and thermal effects tend to counter this alignment. Thus, orientation polarization is highly temperature-dependent, unlike the forms of induced polarization which are nearly temperature-independent. In electric fields of moderate intensity, the orientation polarization is proportional to the local electric field, as for the other forms of polarization... 

Upon, since the permanent electric dipole moment per molecule, Pe, is measurable quantity. The two quantities are related by a relationship similar to the Curie Law, which we shall elaborate upon in Section 6.2 ... 

By analogy with ferromagnetism, ferroelectricity is the property by which a crystal has a permanent electric dipole moment which can be reversed by the application of an electric field. The perovskite BaTiOs, in which the BaO layers are compressed and the Ti02 layers stretched (see Fig. 13.1), is a ferroelectric... 

Molecular electronic dipole moments, pi, and dipole polarizabilities, a, are important in determining the energy, geometry, and intermolecular forces of molecules, and are often related to biological activity. Classically, the pKa electric dipole moment pic can be expressed as a sum of discrete charges multiplied by the position vector r from the origin to the ith charge. Quantum mechanically, the permanent electric dipole moment of a molecule in electronic state Wei is defined simply as an expectation value ... 

Note that since both /z and E are vector quantities, a is a second-rank tensor. The elements of a can be computed through differentiation of Eqs. (9.1) and (9.2). The difference between die permanent electric dipole moment and that measured in the presence of an electric field is referred to as the induced dipole moment. 

In the discussion of many properties of substances it is necessary to know the distribution of atoms or molecules among their various quantum states. An example is the theory of the dielectric constant of a gas of molecules with permanent electric dipole moments, as discussed in Appendix IX. The theory of this distribution constitutes the subject of statistical mechanics, which is presented in many good books.1 In the following paragraphs a brief statement is made about the Boltzmann distribution law, which is a basic theorem in statistical mechanics. 

Fro. IX-1.—Values of the ratio of polarisation P to field strength E for hydrogen chloride gas, as a function of the reciprocal of the absolute temperature. The slope of the line is a measure of the permanent electric dipole moment of the molecules, and the intercept of the line is a measure of the temperature-independent polarizability of the molecules. 

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. 

The quantity in brackets is the permanent electric dipole moment d corresponding to the state i//d [see (1.289)] of course, since both ipei and the operator d depend on the nuclear configuration, the dipole-moment vector d depends on the nuclear configuration. Symmetry requires that d be oriented along the internuclear axis in Fig. 4.1 therefore,... 

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... 

First of all, a molecule must possess a permanent electric dipole moment to exhibit electric-dipole pure-rotation transitions. 

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