Molecular electric dipol

The temporal dynamics of the molecular electric dipole excited by the pulse sequence is shown in Figure 6.5a and b for two distinct values of t. The respective upper frames show the induced dipole oscillation nit) (black dashed line) along with the driving electric field mod(ll ) (gray solid line), the lower frames display... 

Equation (2.81) can be rewritten in terms of derivatives of the molecular electric dipole moment pl j with respect to the Cartesian displacement coordinates, XXa. With... 

Here d is the molecular electric dipole moment, E0 is the amplitude of the drivitt field whose polarization direction defines the z direction, / is the moment of inertiai j of the molecule about an axis perpendicular to the symmetry axis, and A(t/T — ) i the pulse shape function of the form... 

In molecular quantum mechanics, we often find ourselves manipulating expressions so that one of a pair of interacting operators is expressed in laboratory-fixed coordinates while the other is expressed in molecule-fixed. A typical example is the Stark effect, where the molecular electric dipole moment is naturally described in the molecular framework, but the direction of an applied electric field is specified in space-fixed coordinates. We have seen already that if the molecule-fixed axes are obtained by rotation of the space-fixed axes through the Euler angles (, 6, /) = >, the spherical tensor operator in the laboratory-fixed system Tkp(A) can be expressed in terms of the molecule-fixed components by the standard transformation... 

The interaction between the molecular electric dipole moment and an applied magnetic field is represented by the simple operator... 

Second, after an appropriate time interval to allow the gas pulse to reach an optimum position between the cavity mirrors, a 1 qs pulse of monochromatic microwave radiation is introduced into the cavity, which is itself tuned to the correct matching resonant frequency. The pulse carries with it a band of frequencies Av 1 MHz, centred at the resonant frequency v of the cavity. The cavity has a bandwidth of approximately 1 MHz, so that the microwave radiation density is high. If the molecular species under investigation has one or more resonant frequencies within this bandwidth, an appreciable macroscopic polarisation is induced, corresponding classically to a phase-coherent oscillation of the molecular electric dipole moments. The microwave pulse must arrive at the correct time interval after the gas pulse. 

It is, of course, also necessary to calculate the relative intensities of the hyperfine components of each rotational transition in order to assign the spectrum. As we have seen elsewhere, the perturbation due to the interaction of the microwave electric field E(t) with the molecular electric dipole moment may be represented by the effective Hamiltonian... 

The functions X(Q) and Y(fl) are specified by the choice of the particular experiment. Prominent orientational correlation functions result when setting X(Q) = K(Q) = P/(cos0), where P/ is the Legendre polynomial of rank / and the angle 0 specifies the orientation of the molecule with respect to some fixed axis. For example, consider a molecule that possesses a vector property, say the molecular electric dipole p = pu, (u is a unit vector). Then, one defines the dipole autocorrelation function g (t) = (u,(t)u,(0)). Similarly, one defines a correlation function gilt) for second rank tensorial molecular properties. In general the normalized (g/(0) = 1) orientational correlation function of rank l is given by... 

The surface potential is easily predicted to alter the retention behavior of zwitterions. The molecular electrical dipole is subjected to a torque moment that... 

In general, expectation values will be time-dependent due to the time-dependence of the Hamiltonian. However, the expectation value of the molecular electric dipole operator jl is of special interest to us, since it corresponds to the molecular polarization and therefore also to the polarizabilities and hyperpolarizabilities. With help of Eq. (30), the expectation value of jl becomes... 

The bond moment idea falls into the latter category of quantities. It was a very early idea of the chemist that each bond should be assigned a characteristic dipole moment, such that the total molecular electric dipole moment would be obtained by simple vector addition ios-i9) is justified, as has been seen, in so far as... 

Finally, in the third section of this paper, we describe a semiempirical atom dipole model that allows a reliable prediction of molecular electric dipole and quadrupole moments, diamagnetic susceptibilities, and diamagnetic nuclear shieldings. A set of localized bond and atom values are developed for the individual diagonal elements in the total molecular magnetic susceptibility tensor. 

B. Molecular Electric Quadrupole Moments and Molecular Electric Dipole Moment Signs... 

Ets = — (F o X H) acting on the molecular electric dipole moment begins to compete c... 

Subtracting this result from the Lagrangian in Eq. (IV. 13) shows that the (Ro — Wo)-dependence is indeed removed and the field independent contributions which also depend on the velocity of the origin of the molecular coordinate system, Vq — [ o + (ft) X Wo)], add up to the potential energy of the molecular electric dipole moment within a virtual electric Stark-field... 

Polarity is a molecular property. For polyatomic species, the net molecular dipole moment depends upon the magnitudes and relative directions of all the bond dipole moments in the molecule. In addition, lone pairs of electrons may contribute significantly to the overall value of ji. We consider three examples below, using the Pauling electronegativity values of the atoms involved to give an indication of individual bond polarities. This practice is useful but must be treated with caution as it can lead to spurious results, e.g. when the bond multiplicity is not taken into account when assigning a value of x - Experimental values of molecular electric dipole moments are determined by microwave spectroscopy or other spectroscopic methods. 

For a mode of vibration to be infrared (IR) active, it must give rise to a change in the molecular electric dipole moment. 

The theoretical formula of Onsager (J. Amer. Chem. Soc. 1936, 58, 1486) relating the molecular electric dipole moment to the dielectric constant e and refractive index w of a pure polar liquid and to the molar volume V is... 

The light absorption by a molecule is the result of the resonance interaction between the electric field vector of the light and the transition electric dipole of the molecule. This fact tells us that, if the orientation of the molecular electric dipole responsible for the light absorption is aligned and ordered on an electrode surface and if one can control the electric field of the light at the position of the dipole, the optical signal includes information on the molecular orientation. This allows one to estimate the molecular orientation. 

So far, two ways of probing the orientation by ER measurement have been proposed and applied. One of them is based on the direct calculation of the interaction between the electric field of the light and the molecular electric dipole. 

The intensity of an infrared absorption band is proportional to the square of the change in the molecular electric dipole moment p caused by a normal coordinate q ... 

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