Transition electrical interaction

Kobayashi and Saito have studied the sub-millimetre rotational spectra of NF [98] and NCI [99] in their b 1 + states. The measurements for NF were confined to the v = 0 and 1 vibrational levels, and for the lowest rotational transitions, electric quadrupole interaction for the 14N nucleus was observed. Similarly the35 Cl quadrupole interaction was observed for the lowest rotational transitions of NCI. We will compare the data for the three low-lying electronic states in NF and NCI when we discuss their A spectra later in this chapter. 

Electrical interaction also affects transition moments because of the induced dipoles. As shown in Figure 9 for LiH, field gradients with fields may work differently in changing the transition moment of a fundamental versus an overtone transition. 

Finally, one interesting way in which electrical effects are interlaced with vibrational effects is in hydrogen bonding. Intermolecular electrical interaction appears to be a dominant factor in understanding red shifts and transition moment enhancements in intramolecular vibrations of hydrogen-bonded molecules [90, 119, 120]. Undoubtedly, there will be other types of molecular problems that are revealed to be dependent on electrical features. The capability for ab initio study of electrical properties paves the way for this to happen. 

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. 

The other is the use of the Stark effect. The Stark effect arises from the interaction of transition electric dipole with the static electric field at the electrified interface, resulting in a change of the absorption spectrum. Details are given in the following two subsections. 

The Stark effect is the change of absorption spectrum of a dye molecule due to the interaction between the static electric field and the transition electric dipole. The strength of the static electric field at an electrode/solution interface at a certain condition may exceed 10 V m , which is strong enough for the Stark effect to be observed. As for the linear Stark effect, a shift in the absorption spectral band is observed and can be expressed as... 

Electrochemical Stark effect As described already in Section 2.10.2, the Stark effect is based on the interaction of the interfacial static electric field with the transition electric dipole or molecular polarizability. The Stark effect may give rise to the first (or sometimes second) derivative of the absorption spectmm, depending on the type of interaction with the electric field. It is important to note that the ER signal due to the Stark effect should have the same frequency dependence as the ac change of the static electric field insofar as orientation change does not take place simultaneously, because the Stark effect is a field effect. In fact, this has been experimentally confirmed by frequency domain analysis [82]. 

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 interaction between the electrons and the nucleus causes a very small perturbation of the nuclear energy levels in comparison with the energy of the nuclear transition. Such interactions are called hyperfine interactions. The main hyperfine interactions are the following electric monopole, electric quadrupole, and magnetic dipole interactions between the nucleus and the electrons (shell electrons, ligands, etc.). Such interactions can be sensitively monitored by Mbssbauer spectroscopy. The measurement of hyperfine interactions is the key to the utilization of Mbssbauer spectroscopy in a wide range of applications. 

Let us consider the simple case of two ions, each with one excitable electronic state separated from its electronic ground state by nearly equal energy. With suitable interaction between the two electronic systems, the excitation will jump from one ion to the other before a quantum of fluorescence is emitted. The systems interact by Coulomb interactions of the Van der Waals type. Forster (1948), who first treated such a case by quantum-mechanical theory, considered the dipole-dipole interactions. He assumed that the interaction is strongest if, for both transitions, electric-dipole transitions are allowed (Forster 1960). The interaction energy (//sa) is then proportional to the inverse of the third power of the interionic distance, and the transfer probability is given by... 

L. Haggstrom, H. Annersten, T. Ericsson, R. Wappling, W. Karner, S. Bjarman, Magnetic dipolar and electric quadmpolar effects on the Mossbauer spectra of magnetite above the Verwey transition. Hyp. Interact. 5, 201-214 (1978)... 

In contrast to the nonretarded treatment, which is solely based on the electrostatic interaction potential V(r), we equate the electric potential to zero in the retarded case. The electric interaction is completely covered by the vector potential A(r). The transverse modes under investigation enable the Lorentz gauge to be used for vanishing electric potential. This concept turns out especially useful with respect to the Schrodinger formalism presented in the next Chapter. We may ascribe the retarded interaction between electrons located at different particles solely to the vector potential A(r). In addition to providing the proper multipole susceptibilities, quantum theory still has to answer the question regarding statistics. Are the localized modes which are strictly coupled to molecular electron transitions, still Bosons ... 

Three types of electric interactions among a solute and the solvent can be heuristically defined (a) dispersion interactions, (b) interactions due to the transition multipole moments (normally truncated to the transition dipole contribution), and (c) multipolar interactions. Usually, dispersion contributions are simply neglected, whereas the following equations are employed for the evaluation of the shift of absorption energies in terms of polarisability (solute)-dispersion (solvent) (Stark effect), and the polarisability (solute)-polarisability (solvent) interactions, respectively... 

The solutions can be labelled by their values of F and m.p. We say that F and m.p are good quantum. num.bers. With tiiis labelling, it is easier to keep track of the solutions and we can use the good quantum numbers to express selection rules for molecular interactions and transitions. In field-free space only states having the same values of F and m.p can interact, and an electric dipole transition between states with F = F and F" will take place if and only if... 

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