Vector electric dipole

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

The transition probability R is related to selection mles in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection mles (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

In Figure 16.1, we see a pair of point charges Qp, at position vector Fa and <2b at position vector fb. <2a is not necessarily equal to <2b> and one is not necessarily the negative of the other. Their electric dipole moment pe is defined as... 

Table 16.1 Modulus of the electric dipole moment vector of pyridine...

HF-LCAO calculations on molecules with small electric dipoles need to be treated with caution. The classic case is CO. Burrus (1958) determined the magnitude of the vector from a Stark experiment as 0.112 0.005 D (0.374 0.017 x 10-30 Cm). 

Here q is the net charge (monopole), p, is the (electric) dipole moment, Q is the quadrupole moment, and F and F are the field and field gradient d /dr), respectively. The dipole moment and electric field are vectors, and the pF term should be interpreted as the dot product (p F = + EyPy + Ez z)- "I e quadrupole moment and field... 

A point charge +q separated from an equal and opposite point charge —q by a distance d constitutes an electric dipole. An electric dipole has a dipole moment /x, which is a vector with magnitude /x = qd, which is assumed to be acting in the direction from +q to — q (Figure 2.4). 

Based on experiments with linearly polarized light, Mayer also concluded that the photoreceptor is arranged in a dichroic fashion close to the cell wall. The electrical dipole moment for the absorption of bluelight lies parallel to the cell wall, but is probably random with respect to the normal of the cell wall. In the first experiment, the cells were irradiated with bright light. Clearly, the chloroplasts separate from the walls, which are parallel to the -vector and exhibit a banded pattern (Fig. 17, left). However, in weak polarized light the chloroplasts tended to move close to those walls parallel to the -vector (Fig. 17, right). 

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

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... 

The average energy flux in the evanescent wave is given by the real part of the Poynting vector S = (c/47t)ExH. However, the probability of absorption of energy per unit time from the evanescent wave by an electric dipole-allowed transition of moment pa in a fluorophore is proportional to lnfl - El2. Note that Re S and pa E 2 are not proportional to each other they have a different dependence on 0. 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Electric dipole moment studies have provided excellent support for the formulation of certain heterocycles as mesoionic compounds. Hanley et al. <78JCS(P1)600> have measured dipole moments for mesoionic l,2,3,4-thiatriazol-5-imines (20), 5-ones (21) and 5-ylidenemalononitriles (22) using a vector analysis similar to that previously employed for sydnones and other mesoionic compounds assuming that mesoionic rings are regular pentagons. The dipole moment of 3-phenyl-1,2,3,4-thiatriazolium-5-anilide (20) was found to be 3.71 D and five derivatives of compounds (21) were measured and the ring moment calculated to be 3.8 D. In both cases the dipole moments are rather small but clearly consistent with the mesoionic formulation. 3-Phenyl-l,2,3,4-thiatriazolium-5-dicyanomethanide (22) was found to have a dipole moment of 8.84 D. 

The electric dipole operator er is a vector, with components ex, ey, ez). Thus if... 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

VII. Lorenz Vector Potential without Scalar Potential Equivalent Electric Dipole... 

VII. LORENZ VECTOR POTENTIAL WITHOUT SCALAR POTENTIAL EQUIVALENT ELECTRIC DIPOLE... 

Then we have the same electric impulse in both cases. This gives the same electric gauge vector potential, 4,2. However, the Lorenz gauge potentials are quite different. For the electric dipole in Section VI, both 42 and 2 are zero. For the toroidal antenna equivalent electric dipole in Section VII, while 2 is zero, 42 is non zero. How then are these two cases different Within the gauge condition... 

So now we have the question poased in an interesting form. There are two quite different kinds of antennas, both of which produce electric dipole fields, but different Lorenz potentials, one emphasizing the vector potential and the other, the scalar potential. In a classical electromagnetic sense, one cannot distinguish these two cases by measurements of the fields (the measurable quantities) at distances away from the source region. The gauge invariance of QED implies the same in quantum sense. 

So our choices of the two antennas is not unique for separately emphasizing the Lorenz vector and scalar potentials. All that is required is for the two to have the same exterior fields (say, electric dipole fields, or more general multipole fields) with different potentials (related by the gauge condition). In a classical electromagnetic sense, these antennas cannot be distinguished by exterior measurements. This is a classical nonuniqueness of sources. In a QED sense, the same is the case due to gauge invariance in its currently accepted form. 

In the usual texts a multipole expansion involving spherical Bessel functions and spherical vector harmonics is also introduced [16,23,23,26]. The fields from electric and magnetic dipoles correspond to the lowest-order terms ( =1) in the expansion. If we define dipole by this expansion then our toroidal antenna is an electric dipole. In any event, the fields away from the source are the same. This is perhaps a matter of consistency in definitions. 

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. 

Suppose one first considers electric-dipole and magnetic-dipole transitions. As is now well recognized, these are the major contributors to rare-earth absorption and emission spectra. We know that the electric-dipole operator transforms as a polar vector, that is, just as the coordinates (23, 24). This means that it has odd parity under an inversion operation. On the other hand, the magnetic-dipole operator transforms as an axial vector or pseudovector and of course must have even parity (23, 24). 

If we draw an arrow to the coordinate axes to which the symmetry of a given molecule is referred, then the transformation properties of these translation vectors under the symmetry operation of the group are the same as the electric dipole moment Vector induced in the molecule by absorption of light (Figure 3.10). 

Electric dipole radiation is the most important component involved in normal excitation of atoms and molecules. Ttu electric dipole operator has the form TejXf where e is the electronic charge in esu and xt is the displacement vector for the jth electron in the oscillating electromagnetic field. 

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