Electric dipole moments, permanent transition

First of all, a molecule must possess a permanent electric dipole moment to exhibit electric-dipole pure-rotation transitions. 

Symmetric tops with no dipole moment have no microwave spectrum. For example, planar symmetric-top molecules have a C axis and a ak symmetry plane such molecules cannot have a dipole moment. Thus benzene has no microwave spectrum. For a symmetric top with a permanent electric dipole moment, the selection rules for pure-rotation transitions are... 

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

The observed cross sections for the 18s (0,0) collisional resonance with v E and v 1 E are shown in Fig. 14.12. The approximately Lorentzian shape for v 1 E and the double peaked shape for v E are quite evident. Given the existence of two experimental effects, field inhomogeneties and collision velocities not parallel to the field, both of which obscure the predicted zero in the v E cross section, the observation of a clear dip in the center of the observed v E cross section supports the theoretical description of intracollisional interference given earlier. It is also interesting to note that the observed v E cross section of Fig. 14.12(a) is clearly asymmetric, in agreement with the transition probability calculated with the permanent electric dipole moments taken into account, as shown by Fig. 14.6. 

Any molecule with a permanent electric dipole moment can interact with an electromagnetic field and increase its rotational energy by absorbing photons. Measuring the separation between rotational levels (for example, by applying a microwave field which can cause transitions between states with different values of /) let us measure the bond length. The selection rule is A/ = +1—the rotational quantum number can only increase by one. So the allowed transition energies are... 

In practice values of B are also often quoted in cm-1. For the simple rigid rotor the rotational quantum number J takes integral values, J = 0, 1, 2, etc. The rotational energy levels therefore have energies 0, 2B, 6B, 12B, etc. Elsewhere in this book we will describe the theory of electric dipole transition probabilities and will show that for a diatomic molecule possessing a permanent electric dipole moment, transitions between the rotational levels obey the simple selection rule A J = 1. The rotational spectrum of the simple rigid rotor therefore consists of a series of equidistant absorption lines with frequencies 2B, 4B, 6B, etc. 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

Notice a very important feature of equation (6.334). Electronic transitions do not depend for their intensity on the presence of a permanent electric dipole moment in the molecule, so that they exist for both homonuclear and heteronuclear diatomic molecules. This is in contrast to rotational and vibrational transitions which have electric dipole intensity only in heteronuclear molecules (apart from one extraordinary exception for the II2 molecule, described in chapter 10.)... 

Figures 6 and 7 show absorption and electroabsorption spectra of [ (NH3)5Ru 2(/A-pyz)]5+ and [ (NH3)5Ru 2(M,4 -bpy)]5+, respectively. The change in AA as a function of x is uniform for the bands, which indicates that the molecular properties that give rise to AA are identically oriented with respect to the transition dipole moment. The electroabsorption spectra in the near-IR region (MMCT bands) give the greatest differences between complexes when analyzed with Eq. (31) and these are shown in Fig. 8. For the Creutz-Taube ion (Fig. 8A), the spectrum does not satisfactorily reduce to a sum of derivatives but nevertheless shows that AA(p) line shape to be modeled primarily by a negative zeroth derivative (Ax) term, especially at energies below 6500 cm-1. The fit in this case yields a value for Ap. = 0.7 0.1 D, which when compared with the maximum permanent electric dipole moment ( A/u max = 32.7 D, assuming a metal-to-metal distance) is strong evidence for a delocalized ground state. Contrast this result with the analysis of the electroabsorption spectrum of [ (NH3)5Ru 2(ja-4,4 -bpy)]5+ shown in Fig. 8B.

Although 3IIoe can mix with many excited 1E+ states, mixing with the X1E+ state introduces a novel feature, namely, the appearance of permanent electric dipole moments as well as transition moments in the intensity borrowing model. For 3II in the case (a) limit (A > 21/2BJ),... 

The molecule PH3 (C3V symmetry) is an oblate symmetric top (Crotational constants C (refers to rotation around the C3 axis) and B (perpendicular to C3). Since the permanent electric dipole moment is pointed parallel to the C3 axis, only pure rotational transitions with the selection rule AK=0 are allowed (K is the quantum number of the component about the C3 axis of the total angular momentum J). Their analysis leads to the parameters B, Dj, Djk, and Hjk. From the perturbation-allowed transitions AK= 3n (n=1,2,...), which become weakly allowed by centrifugal distortion effects (inducing a small dipole moment of about 8x10 D perpendicular to the C3 axis [1, 2, 3]), the K-related constants (C, Dk, Hk) were obtained see, e.g. [1, 3, 4]. 

Finally, there is a way to use fixed frequency lasers for spectroscopy if one can achieve the tuning on the side of the molecules. Species with a permanent magnetic or electric dipole moment can be tuned into resonance by the Zeeman - or Stark-effect respectively. Tunability is very limited and therefore a densely distributed series of fixed frequency laser transitions is necessary for complete coverage of the spectrum. 

It was pointed out independently by Williams (1967) and Culvahouse et al. (1967) that for a non-Kramers ion at a site lacking in full inversion symmetry, terms linear in an electric held may exist for a doublet state. Thus for Cj, symmetry (but not for C y) the system may have a permanent electric dipole moment, and its interaction with an electric held may be represented by additional terms of the form -I- SyEy). Transitions then occur with an RF electric held normal to the z-axis, even in the absence of a distortion from axial symmetry. As before, random distortions again produce an asymmetrical line shape, but with a maximum corresponding to the point for zero distortion, unlike the magnetic transitions referred to above. The asymmetry is present because in each case the distortions move the transitions to higher frequency at constant applied held, or to lower held at constant frequency. Such electric dipole moments also give rise to electric interactions between the ions (see section 5.6). 

The unit cells in the lattice of the lower-symmetry phases that are stable below the Curie temperature have ea permanent electrical dipole moment. In analogy with the magnetic phases, these are called ferroelectric if the moments are coupled in parallel and antiferroelectric if they are antiparallel. When the temperature is decreased to below the Curie temperature the symmetry becomes lower than cubic, the inversion center disappears, and the compound becomes piezoelectric. Figure 4.24 shows the change in properties at the phase transition of BaTi03. Further down... 

Piezoelectricity and ferroelectricity are the result of electric dipole effects that are due to ions shifting from their initial positions in the lattice. This effect, which is strongly structure-dependent, was discussed above. Pyroelectric materials have permanent electric dipole moments, their magnitude varying with temperature. In infrared detectors, use is made of the ferroelectric phase transitions in perovskites. 

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