Electric dipole moment, component

The electric dipole moment components of the dipole of the THP-H20 complex have been determined using Stark-effect FT microwave spectroscopy. Only a- and c-type spectra were observed, which is consistent with computational studies <1998CPL(297)543>. 

Electric dipole moments components can be calculated from Stark effect measurements [Eqn. (3)], and the results for dimers are collected in Table 4. As shown by Eqn. (3), these experiments give the dipole moment components projected along the principle axes of inertia, but do not directly give the total moment of the molecule. Many of the molecules in Table 4 have A rotational constants which are very large, and thus the Stark effects are dominated by the a-component of the dipole moment in Eqn. (3). For example, p for H2S HF is accurately determined to be 2.6239(17)D, but only the combination px = (p + p2)1/2 = 0.97(20)D can be found for the remaining components. 341 The total molecular moment is then roughly 2.80(7)D. 

Table 4. Electric dipole moment components and the enhancement, Ap of the dimer p, over vector addition of free monomer moments.

Table 14 Superimposition of the pyrocatechin G NRG (capital letters) and the Civ symmetry point (small letters) character tables, with their representations in trigonometric basis sets, as well as the electric dipole moment components...

In the same table the representations of the G4 and Cqu groups, in trigonometric basis sets are given, as well as the electric dipole moment components. So, it is seen that the z, x and y electric dipole components transform according the /li, Ai and representations of the G4 group, respectively. 

The polarizability in (1) is conveniently expressed in terms of the second-order matrix element of the electric dipole moment component Dz... 

The electric dipole moment components are necessarily used in estimating relative conformational abundances, as is explained below. The predicted values of the electric dipole moment components of the threonine conformers are collected in Table 1. 

A, B, and C are the rotational constants Xaa. Zbb. and Xcc are the diagonal elements of the nuclear quadrupole coupling tensor Pa. Fb. and are the electric dipole moment components... 

According to the values of the predicted electric dipole moment components and rotational constants listed in Table 1, the rotational spectra of most of the threonine conformers are dominated by pa-type, R-branch transitions forming groups of lines with characteristic patterns which appear at frequency intervals equivalent to B -f C. Wide frequency scans with low power polarization conditions were conducted to search for such rotational transitions of conformers with relatively large pa- Several sets of R-branch lines corresponding to five different rotamers are labeled L, M, N, O, and P. Spectral searches, conducted to detect other sets of pa-type R-branch transitions, using high microwave power for polarization, were unsuccessful. Therefore, wide frequency scans were carried out to identify pu- and pc-type transitions. Finally, two more rotamers labeled Q and R were identified. 

This applies for any class of rotor with f> the fraction of molecules in the lower state 7, t of the transition and the vibrational state v pg is the electric dipole moment component giving rise to the particular transition under observation, c is the speed of light k is the Boltzmann constant T is the absolute temperature of the gas, vq is the frequency for which the absorption is a maximum x is the mole fraction of the absorbing molecular species p is the total pressure in the absortion cell and Av is the half-width of the line. The above expression summarizes the various factors that affect the line intensity. Since Av is proportional to p, o is independent of total pressure. Furthermore, the intensity increases with frequency, dipole moment, and kg (7, t 7, t ), the line strength of the transition. This latter quantity is related to the transition moment by... 

The electric dipole moment operator jx has components along the cartesian axes ... 

For any molecular vibration that leads to infrared absorption, there is a periodic change in electric dipole moment. In case the direction of this change is parallel to component of the electric vector of the infrared radiation, absorption takes place otherwise it does not. In oriented bulk polymers, the dipole-moment change can be confined to specified directions. The use of polarised infrared radiation in such a case leads to absorption which is a function of the orientation of the plane of polarisation. The... 

In the ideal case of free Eu + ions, we first must observe that the components of the electric dipole moment, e x, y, z), belong to the irreducible representation in the full rotation group. This can be seen, for instance, from the character table of group 0 (Table 7.4), where the dipole moment operator transforms as the T representation, which corresponds to in the full rotation group (Table 7.5). Since Z)° x Z) = Z) only the Dq -> Fi transition would be allowed at electric dipole order. This is, of course, the well known selection rule A.I = 0, 1 (except for / = 0 / = 0) from quantum mechanics. Thus, the emission spectrum of free Eu + ions would consist of a single Dq Ei transition, as indicated by an arrow in Figure 7.7 and sketched in Figure 7.8. 

The resulting property operators at the four-component relativistic level are listed in Table 1. From the property operators associated with uniform electric and magnetic fields one may directly read off the relativistic operators of electric dipole moment p,= —r, and magnetic dipole moment m = — c(r,o X a,), respectively [36]. 

The integrations over the electronic coordinates contained in < >, as well as the integrations over vibrational degrees of freedom yield "expectation values" of the electric dipole moment operator because the electronic and vibrational components of i and [Pg.287]

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... 

The probability of a transition being induced by interaction with electromagnetic radiation is proportional to the square of the modulus of a matrix element of the form where the state function that describes the initial state transforms as F, that describing the final state transforms as Tk, and the operator (which depends on the type of transition being considered) transforms as F. The strongest transitions are the El transitions, which occur when Q is the electric dipole moment operator, — er. These transitions are therefore often called electric dipole transitions. The components of the electric dipole operator transform like x, y, and z. Next in importance are the Ml transitions, for which Q is the magnetic dipole operator, which transforms like Rx, Ry, Rz. The weakest transitions are the E2 transitions, which occur when Q is the electric quadrupole operator which, transforms like binary products of x, v, and z. 

The main purpose of this section is consideration of the FIR spectra due to the second dipole-moment component, p(f). However, for comparison with the experimental spectra [17, 42, 51] we should also calculate the effect of a total dipole moment ptot. In Refs. 6 and 8 the modified hybrid model44 was used, where reorientation of the dipoles in the rectangular potential well was considered. In this section the effect of the p(f) electric moment will be found for the hat-curved, potential, which is more adequate than the rectangular potential pertinent to the hybrid model. In Section VI.B we present the formula for the spectral function of the hat-curved model modified by taking into account the p(f) term (derivation of the relevant formula is given in Section VI.E). The results of the calculations and discussion are presented, respectively, in Sections VI.C and VI.D. 

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