Radiative coupling

Of course, each of the terms in (5.3) is a function of the internal coordinates of the molecule. For the case we consider, the interaction terms in (5.2), which control the transfer of amplitude between the two electronic manifolds, only contain the radiative coupling term... 

Although not sufficient to ensure enantiomeric selectivity, the ultimate conse-quence of this difference is that populations of f D) and EL) after laser excitation are different when there is radiative coupling between levels IE)) and E2). 

S - The continuum component (e ]E, n-) is therefore driven by the bound state times the radiative coupling term. Driven equations of the type written here are implicitly 5%sed in all practical computational schemes developed for weak-field molecular hotodissociation problems [14, 26],... 

The results in this section make clear that a chiral outcome, the enhancement of a particular enantiomer, can arise by coherently encoding quantum interference information in the excitation of a racemic mixture. The fact that the initial state displays a broken symmetry and that the excited state has states that are either symmetric or antisymmetric with respect to (Th allows for the creation of a superposition state that does not have these transformation properties. Radiatively coupling the states in the superposition then allows for the transition probabilities from L and D to differ, allowing for depletion of the desired enantiomer. 

As briefly mentioned in the Introduction the MEF phenomenon is a result of the interactions between the excited states of the fluorophores and the induced surface plasmons of metal nanopaiticles or roughened surfaces. Figure 1.2A depicts our laboratory s interpretation of the processes involved in the interactions of fluorophores with metal nanoparticles in close proximity to one another. There are two main processes thought responsible in MEF 1) non-radiative coupling from the excited state of the fluorescent species to surface plasmons of the metallic... 

The intense luminescence of (Ir(2 = phos)2)C10 [2 = phos -e/s -1,2-bis(diphenylphosphino)ethylene in a rigid glass matrix at 9.5 K has been monitored while external magnetic fields were applied. Radiative coupling to the ground state from a forbidden component was induced by the field.Decay curves of emission from c/5-[ IrCljCbpy) jJCl, c/s-[ IrCl2(phen)2)Cl,... 

To see this connection in more detail we extend the model of Figs 9.1 and Eq. (9.2) to include two discrete states, the ground state g) and an excited state lx), and a continuum of states I/) that may represent the ground state dressed by environmental or radiation field states. We assume that l ) is the only excited state in the relevant spectral region that is radiatively coupled to the ground state g) so it can be initially prepared as explained in Section 9.2.4. In the subspace that encompasses the state [s ) and the continuum Z), the former plays the same role as state 11) in Fig. 9.1. We now focus on the excitation from g to s specifically we pose the question What is the corresponding absorption lineshape ... 

Note the subtle difference between this radiative coupling which is a sum over all modes of the radiation field, and the coupling (9.39d) which involves only the particular mode that enters in state 0>. 

Problem 18.2. A well-known result from the theory of optical absorption lineshapes is that the integrated lineshape associated with the transition between two quantum levels is equal, up to known numerical factors, to the squared radiative coupling element between these levels. For example, using Eq. (18.9) or (18.10) yields / dcoLlai ) o< /zi,2l. Show that, under the Condon approximation, the integrated absorption lineshape of an overall transition between two vibronic manifolds of two electronic states 1 and 2 is also proportional to the squared radiative electronic coupling l/xp2p. 

Figure 5. Pictoral representation of the Liouville space pathways that contribute to the nonlinear response function [Eqs. (49) and (53)]. Solid lines denote radiative coupling V, horizontal (vertical) lines represent action of V from the right (left). Starting at aa, after three perturbations, the system finds itself along the dashed line. The dotted lines represent the last V, which acts from the left. At the end of four perturbations, the system is in a diagonal state (aa, bb, cc, or dd). The number of three-bond pathways leading to ad, ba, dc, and cb is 1, 1,3, and 3, respectively. Altogether, there are, therefore, eight pathways, which are shown in Fig. 6. In each pathway, each of the three incoming fields acts once.

Figure 7. Pictorial representation of the pathways in Liouville space that contribute to SRF spectra. Solid lines denote radiative coupling V. Horizontal (vertical) lines represent action of V from the right (left). The SRF process is obtained by all pathways that start at aa and end at cc in fourth order (four bonds). There are six pathways that contribute. However, owing to symmetry, we need consider only the three pathways shown in Fig. 8. The other three are obtained by a complex conjugation and permutation of b and d.

Case A - small detuning A=lug-wg << fi(R(0), where tlfi is the retarded dipole-dipole interaction (radiative coupling) which varies as for C<<1. This inequality is satisfied by all diatoms wherein A and B are isotopic species, as well as by systems such as Na(5p->-3s )+Mg( So- - Pi). 

Here hnn represents the vibrational Hamiltonian of the ionic state and the index k labels the energy Ek of the continuum electrons. In addition, we generalize the molecule-field interaction to allow for radiative couplings between 4>o) and jTf) (for simplicity, it is assumed that Tf) is dark in absorption) and for radiative couplings between the excited states f),... 

Therefore equation (2.1) can be rewritten, neglecting the radiative coupling terms ... 

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