Rotation-electron coupling

I should have mentioned that in this example only one vibrational channel is included in the calculations, that is, only rotation-electron coupling is taken into account. Vibration-electron coupling will be discussed in the second part of my talk. 

This is an important result. The first term leads to the rotational eigenvalues, whilst the second term describes the rotational electronic coupling and, as we shall see, contributes to the rotational magnetic moment and the spin rotation interaction. The third term is small and can be neglected for states where A = 0. We have omitted the electron kinetic energy term from (8.101) because it is part of the zeroth-order Hamiltonian which determines the electronic eigenvalues and eigenfunctions. 

Many of the observed levels have measured g-factors which are closer to the pure case (c) values than to any alternative pure coupling case. However there is extensive rotational electronic coupling which, in many instances, mixes the case (c) states case (e) is then a better limiting basis, as we shall see in due course. First we investigate the electric dipole transition probabilities for the Zeeman components, so that we can understand the pattern of lines illustrated in figure 10.73. 

Dipole-bound anions (5a, 4f) in which the extra electron is attracted primarily by the dipole force field of the polar molecule and for which rotation-to-electronic coupling is most important in inducing electron ejection. 

NH (X n) for which (4d) vibration of the N-H bond couples only weakly to the non-bonding 2pn orbital and for which rotation-to-electronic coupling can be dominant in causing electron ejection for high rotational levels. 

As with U and Np ions, flow coulometry experiments were conducted to further study the electrode reactions of Pu ions in acidic aqueous solutions [49]. The results from these studies confirm the reversibility of the one-electron couples Pu02 " /Pu02 and Pu" /Pu " " in nitric, perchloric, and sulfuric acid solutions. The further reduction of Pu02 resulted in an irreversible two-electron transfer yielding Pu +. The flow coulometry results in the mixed phosphoric-nitric acid solutions confirm the overall conclusions that have been reached from the stationary and rotated working electrode experiments described previously, in which PuO + is the primary Pu(IV) product from Pu02 reduction. 

The well-known selection rules proposed by Woodward and Hoffman25 to predict the stereochemical course of electrocyclic reactions can be viewed as emphasizing the symmetry requirements for electronic coupling of final and initial states. The rules are expressed in terms of rotatory motions required to convert one electronic state into another, so the matrix element is really vibronic rather than pure electronic. In terms of this paper, it appears that Woodward and Hoffman have identified necessary rotation properties of the perturbation operator. 

Equation (33) is only an approximation for real molecules in that it assumes both a single value for r and structureless, spherical reactants. In fact, it has been suggested for Fe(H20)63+/2+ selfexchange that a significant feature of the reaction may be the interpenetration of the coordination spheres in order to enhance electronic orbital overlap.12 In addition, for low-symmetry cases, electronic coupling can have an angular dependence if rotational correlation times within the... 

The application of surface-enhanced Raman spectroscopy (SERS) for monitoring redox and other processes at metal-solution interfaces is illustrated by means of some recent results obtained in our laboratory. The detection of adsorbed species present at outer- as well as inner-sphere reaction sites is noted. The influence of surface interaction effects on the SER spectra of adsorbed redox couples is discussed with a view towards utilizing the frequency-potential dependence of oxidation-state sensitive vibrational modes as a criterion of reactant-surface electronic coupling effects. Illustrative data are presented for Ru(NH3)63+/2+ adsorbed electrostatically to chloride-coated silver, and Fe(CN)63 /" bound to gold electrodes the latter couple appears to be valence delocalized under some conditions. The use of coupled SERS-rotating disk voltammetry measurements to examine the kinetics and mechanisms of irreversible and multistep electrochemical reactions is also discussed. Examples given are the outer- and inner-sphere one-electron reductions of Co(III) and Cr(III) complexes at silver, and the oxidation of carbon monoxide and iodide at gold electrodes. 

The indirect spin-spin coupling is independent of molecular rotation. The coupling mechanism is known to involve the electron spins of the bonding electrons and is the result of a weak electron polarization. The interaction energy AX is proportional to the scalar product of the nuclear spins / of A and X, according to the following expression ... 

In the foregoing discussion it is necessary to consider that the coupling is represented by a scalar Jax term. This is usually valid in solution where the molecule is rotating rapidly and randomly, and therefore electron-coupled interactions are isotropic. In other cases, the coupling must be treated as a second-rank tensor /AX. 

Figure 1.10. (a) Second-order spin-rotation interaction occurring via L. (b) Second-order pseudo-contact hyperfine interaction occurring via L. (c) Electron coupled nuclear spin-spin interaction, (d) Second-order interaction of R and L. 

As mentioned above, the terms which are responsible for the coupling of the 25+1 n state to the 25+1 states are the spin-orbit coupling and the rotational electronic Coriolis term. Thus in the second-order perturbation expression in equation (7.43), the perturbation term is... 

We have chosen to use the hyperfine-coupled representation, where for 12CH, F is equal to J 1 /2. An appropriate basis set is therefore t], A N, A S, J, /, F), with MF also important when discussing Zeeman effects. As usual the effective zero-field Hamiltonian will be, at the least, a sum of terms representing the spin-orbit coupling, rigid body rotation, electron spin-rotation coupling and nuclear hyperfine interactions, i.e. 

---