Dipole moment vector

The response of a medium to a macroscopic field E(t) generated by the superposition of a static and an optical component (E(f) = E° + E cos(< h)) is represented by the dielectric polarization vector (dipole moment per unit of volume) P(t) ... 

P is the dielectric polarization vector (dipole moment per volume, C m m = C m ) induced by the electric field and M the magnetization vector (magnetic dipole moment per volume, A m ) induced by the magnetic field. The constants in (5) and (6) are the vacuum permittivity o = 8.85419 x 10 C m and the vacuum permeability ixq = AttX 10 V s m It is implied by (5) and (6) that the response of the medium is purely local (dipole approximation). 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

There are other important properties tliat can be measured from microwave and radiofrequency spectra of complexes. In particular, tire dipole moments and nuclear quadmpole coupling constants of complexes may contain useful infonnation on tire stmcture or potential energy surface. This is most easily seen in tire case of tire dipole moment. The dipole moment of tire complex is a vector, which may have components along all tire principal inertial axes. 

Measurements of Stark splittings in microwave and radiofrequency spectra allow tliese components to be detennined. The main contribution to tire dipole moment of tire complex arises from tire pennanent dipole moment vectors of tire monomers, which project along tire axes of tire complex according to simple trigonometry (cosines). Thus, measurements of tire dipole moment convey infonnation about tire orientation of tire monomers in tire complex. It is of course necessary to take account of effects due to induced dipole moments and to consider whetlier tire effects of vibrational averaging are important. 

Figure 4-16 Orientation of Dipole Moment Vectors to give Vj,.

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

Figure 7-1 Dipole Moment Vectors for Methylcnccyclopropcne. Bv convention, the dipole moment arrow is draw-n in the negative direction.

The result of all of the vibrational modes contributions to la (3 J-/3Ra) is a vector p-trans that is termed the vibrational "transition dipole" moment. This is a vector with components along, in principle, all three of the internal axes of the molecule. For each particular vibrational transition (i.e., each particular X and Xf) its orientation in space depends only on the orientation of the molecule it is thus said to be locked to the molecule s coordinate frame. As such, its orientation relative to the lab-fixed coordinates (which is needed to effect a derivation of rotational selection rules as was done earlier in this Chapter) can be described much as was done above for the vibrationally averaged dipole moment that arises in purely rotational transitions. There are, however, important differences in detail. In particular. 

Here r is the vector giving, together with e, the unit charge, the quantum mechanical dipole moment operator... 

Molar absorptivity (Section 13 21) Ameasure of the intensity of a peak usually in UV VIS spectroscopy Molecular dipole moment (Section 1 11) The overall mea sured dipole moment of a molecule It can be calculated as the resultant (or vector sum) of all the individual bond di pole moments... 

In the examples shown in Figures 4.18(a)-4.18(g) all the molecules clearly have a charge asymmetry and, therefore, a non-zero dipole moment. Since a dipole moment has magnitude and direction it is a vector quantity and, if we wish to emphasize this, we use the vector symbol /x, whereas if we are concerned only with the magnitude we use the symbol /r. 

Charge asymmetry can be associated with a particular bond in a molecule and gives rise to what is called a bond dipole moment or, simply, bond moment. One use of bond moments is that they can be transferred, to a fair degree of approximation, from one molecule to another. In this way the dipole moment of a molecule can sometimes be estimated from a vector sum... 

The dipole moment vector /i must be totally symmetric, and therefore symmetric to all operations of the point group to which the molecule belongs otherwise the direction of the dipole moment could be reversed by carrying out a symmetry operation, and this clearly cannot happen. The vector /i has components fiy and along the cartesian axes of the molecule. In the examples of NH3 and NF3, shown in Figures 4.18(b) and 4.18(e), respectively, if the C3 axis is the z-axis, 7 0 but = 0. Similarly in H2O and cis-... 

If we compare the vectors representing a translation of, say, the H2O molecule along the z-axis, as illustrated in Figure 4.14(a), with the dipole moment vector, which is also along the z-axis and shown in Figure 4.18(a), it is clear that they have the same symmetry species [i.e. T(piJ = T T )] and, in general. 

Since the dipole moment is a vector in a particular direction it has the same symmetry species as a translation of the molecule in the same direction. Figure 6.21 shows this for FI2O in which the dipole moment and the translation in the same direction have the same symmetry species, the totally symmetric dj species. In general. 

Figure 6.21 (a) the dipole moment vector for H2O and (b) a translation in the same direction... 

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