Electric moment first

Whilst the electric moment so calculated is in reality not an absolute value since it is actually only the alteration in electric moment of the surface produced by substituting the adsorbed solute molecules for solvent molecules, yet it is clear that the ionisable substances possess large values which vary within wide limits as the surface concentration is altered. We must conclude that since the apparent molecular electric moment varies with the concentration that Helmholtz s conception of a rigid double layer must be replaced by some species of boundary layer which varies in structure with the surface concentration. Gouy loo. cit) was the first to consider in detail the mechanism by which the ions are kept away from the charged surface. He put forward the view that the finite value of S is due to their thermal agitation. On this M... 

The fact that the El approximation to (Xfy contains matrix elements of the electric dipole operator between the initial and final states makes it clear why this is called the electric dipole contribution to af5i within the El notation, the E stands for electric moment and the 1 stands for the first such moment (i.e., the dipole moment). 

Analogous quantities to die electric moments can be defined when the external perturbation takes the form of a magnetic field. In this instance die first derivative defines the permanent magnetic moment (always zero for non-degenerate electronic states), the second derivative the magnetizability or magnetic susceptibility, etc. 

The first attempt to formulate a theory of optical rotation in terms of the general equations of wave motion was made by MacCullagh17). His theory was extensively developed on the basis of Maxwell s electromagnetic theory. Kuhn 18) showed that the molecular parameters of optical rotation were elucidated in terms of molecular polarizability (J connecting the electric moment p of the molecule, the time-derivative of the magnetic radiation field //, and the magnetic moment m with the time-derivative of the electric radiation field E as follows ... 

However, Eq. (2.21) is not very convenient in the context of intramolecular electrostatic interactions. In a protein, for instance, how can one derive the electrostatic interactions between spatially adjacent amide groups (which have large local electrical moments) In principle, one could attempt to define moment expansions for functional groups that recur with high frequency in molecules, but such an approach poses several difficulties. First, there is no good experimental way in which to measure (or even define) such local moments, making parameterization difficult at best. Furthermore, such an approach would be computationally quite intensive, as evaluation of the moment potentials is tedious. Finally, the convergence of Eq. (2.20) at short distances can be quite slow with respect to the point of truncation in the electrical moments. 

The first term in the square bracket in this equation is the electric monopole moment, which is equal to the nuclear charge, Ze. The second term in the square bracket is the electric dipole moment while the third term in the square bracket is the electric quadmpole moment. For a quantum mechanical system in a well-defined quantum state, the charge density p is an even function, and because the dipole moment involves the product of an even and an odd function, the corresponding integral is identically zero. Therefore, there should be no electric dipole moment or any other odd electric moment for nuclei. For spherical nuclei, the charge density p does not depend on 0, and thus the quadmpole moment Q is given by... 

Prior to about 1955 much of the nuclear information was obtained from application of atomic physics. The nuclear spin, nuclear magnetic and electric moments and changes in mean-squared charge radii are derived from measurement of the atomic hyperfine structure (hfs) and Isotope Shift (IS) and are obtained in a nuclear model independent way. With the development of the tunable dye laser and its use with the online isotope separator this field has been rejuvenated. The scheme of collinear laser/fast-beam spectroscopy [KAU76] promised to be useful for a wide variety of elements, thus UNISOR began in 1980 to develop this type of facility. The present paper describes some of the first results from the UNISOR laser facility. 

Although the change in the quadrupole moment of OH expressed by equation (123d) (the first nonzero permanent electric moment is always independent of the choice of origin21 ) was not taken into account in building up the H02 DMBE potential of ref. 141, it is likely that the associated error will have no practical significance. 

The first term in (3.296) is the usual Stark interaction while the second term vanishes for a neutral molecule. We have met the third term before in section 3.4 one physical explanation of its occurence is that a moving spin magnetic moment creates an electric moment perpendicular to both its direction and its velocity which interacts with the applied electric field. 

Diagonalisation of the Stark matrices enables us to plot the Stark energies, given values of B and /M), and the results are shown in figure 8.27 for the first three rotational levels, J = 0, 1 and 2. The parameter X is defined by A.2 = iJ E jB. In figure 8.28 we show plots of the effective electric moment of the molecule in the different J, M states listed in figure 8.27. With the aid of both diagrams, we are able to understand the principles of electric state selection, and the electric resonance transitions. 

The dispersion attractive interactions were first characterized by London (1930) and arise from the rapid fluctuations in electron density in one atom, which induce an electrical moment in a neighbouring atom. By making use of quantum-mechanical perturbation theory, London arrived at the well-known expression for the potential energy, eD(r), of two isolated atoms separated by a distance r ... 

As well known, the NRG of acetone is the Gae. The first step should be to determine the representations of the Gae group under whidi the electric moment components transform. For that purpose, let us consider acetone in a molecular axis system, in which the z axis coincides with the Ga axis of the molecule, the y axis lies perpendicular to z axis in the CCC plane, and the x axis stands perpendicular to the CCC plane. 

The resultant (vector sum) electric moment of the medium per unit volume is known as the polarization P. Eor an isotropic medium, P is parallel to the electric field intensity E, and to a first approximation it is proportional to E in magnitude. For a pure substance, P is given by... 

One reason for this at first sight unexpected result is the fact that probably 70... 90% of the solute/solvent interaction term is caused by London dispersion forces, which are more or less equal for the cis and trans isomers. Another important reason is that one has to take into account higher electric moments the trans isomer has a quadrupole moment, and the cis isomer also has moments of a higher order than two. Calculations of solute/solvent interactions of both diastereomers using a reaction field model led to the conclusion that the quadrupolar contribution of the trans isomer is comparable to the dipolar contribution of the cis isomer. It has been pointed out that the neglect of solute/solvent interactions implying higher electric moments than the dipole moment can lead to completely false conclusions [202],... 

Specifically, octahedrally symmetric molecules like SF have, as their first electric moment, a hexadecapole, since all the lower moments vanish as a result of high symmetry (p = 0 = 2 = 0). 

For tetrahedral molecules the linear polarizability is isotropic, and the first non-zero permanent electric moment is the octupole Q = TlJe electric fields of these octupoles induce a dipole moment in any given molecule, whence 0 and we have by equation (241) to a suflBciently good approximation ... 

In the case of tetrahedral symmetry, the dipole and quadrupole moments vanish (p — 0 = 0) the first (lowest) non-zero electric moment is octupolar and can be written thus ... 

In order to test the apparatus the first substances investigated were those for which the electric moment was already known from... 

These results having been obtained, the method was used to investigate a problem of fundamental importance in the realm of chemical constitution. According to Weissenberg s theory, substances of the type Ca, i.e. methane derivatives with all four substituents the same, should not only be able to exist in the form of a regular tetrahedron, but there should also exist molecular forms in which the C-atom is situated at the vertex of a pyramid and the four substituents at the four corners of the base. Molecules with the first type of structure should have no electric moment, whereas those with the second type should exhibit a permanent dipole moment. Pentaerythritol, C(CH20H)4, is frequently quoted as an example of the second type of structure. The moment of this substance cannot be found by the dielectric-constant method, as it... 

Each molecule is characterized by its first two observable electric moments (quadrupole alone for centrosymmetric molecules, terms higher than R s not being considered in the formulation of the model). 

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