Transitions between electronic states

Electron states in a crystal with space group G are described by state functions that belong to one of the IRs of G 

Not all such pairs Ra, Rb will do but only those pairs for which 

On summing over translations, it follows from the orthogonolity theorem for the characters of the IRs of the translation group that 

Here both k, and k, refer to the symmetry point M. We thus need to see which possible prongs of the star of M in eqs. (12) will satisfy eq. (9). This is summarized in Table 17.17. The column headed = k shows that the only possible k vectors k/ are T and M. (A star is fully determined by any one of its members, say M, so that the pairs Ra, Rb that give M2, M3 

The column headed = k lists all possible wave vectors that could result from summing a member of the star of k, with one from the star of kj. Not all of these yield k7 because of the restriction imposed by eq. (17.8.9), that is by translational symmetry. 

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Figure Al.6.21. Bra and ket wavepacket dynamics which detennine the coherence overlap, (( ) ( ) ). Vertical arrows mark the transitions between electronic states and horizontal arrows indicate free propagation on the potential surface. Full curves are used for the ket wavepacket, while dashed curves indicate the bra wavepacket. (a) Stimulated emission, (b) Excited state (transient) absorption (from [41]).

The measurements are predicted computationally with orbital-based techniques that can compute transition dipole moments (and thus intensities) for transitions between electronic states. VCD is particularly difficult to predict due to the fact that the Born-Oppenheimer approximation is not valid for this property. Thus, there is a choice between using the wave functions computed with the Born-Oppenheimer approximation giving limited accuracy, or very computationally intensive exact computations. Further technical difficulties are encountered due to the gauge dependence of many techniques (dependence on the coordinate system origin). 

Transitions occur constantly in nature molecules change from one tautomeric form to another, radioactive nuclei decay to form other nuclei, acids dissociate, proteins alter their shapes, molecules undergo transitions between electronic states, chemicals react to form new species, and so forth. Transition rules allow the simulation of these changes. 

The emission spectrum of some PT and PBD polymer bilayer devices cannot be explained by a linear combination of emissions of the components. Thus, white emission of the PLEDs ITO/422/PBD/A1 showed Hof 0.3% at 7 V, and consisted of blue (410 nm), green (530 nm), and red-orange (620 nm) bands. Whereas the first and the last EL peaks are due to the EL from the PBD and the PT layers, respectively, the green emission probably originates from a transition between electronic states in the PBD layer and hole states in the polymer... 

In considering absorption of light by molecules, we have been principally concerned with transitions between electronic states. However, it is not possible to explain fully the effects of electronic excitation in molecules unless we also take into account the motions of the nuclei. 

Radiative and non-radiative transitions between electronic states... 

Radiative and non-radiative transitions between electronic states 39 Box 3.2 Spontaneous and stimulated emissions... 

The simplest approach to understanding the radiation- (light-) induced transition between electronic states is to invoke time-dependent perturbation theory. Thus, one starts from the time-dependent Schrodinger equation... 

Figure 3.23 Jablonski diagram of the transitions between electronic states of a polyatomic molecule. Hc> stands for internal conversion, isci for intersystem crossing, V and (a for absorption of light, f for fluorescence and (p> for phosphorescence...

We have seen that transitions between electronic states of different spin quantum numbers are in principle forbidden by the law of conservation of angular momentum. In practice these transitions take place only through the compensation of two simultaneous changes in angular momentum represented by the orbital quantum number L and the spin quantum number S their sum J=L + S remains constant while L and S vary in opposite directions. 

The dynamics of nuclei on PES s and the transitions /—> / between electronic states, can be described with either a time-independent or a time-... 

Transitions between electronic states are formally equivalent to transitions between different vibrational or rotational states which were amply discussed in Chapters 9 11. Computationally, however, they are much more difficult to handle because they arise from the coupling between electronic and nuclear motions. The rigorous description of electronic transitions in polyatomic molecules is probably the most difficult task in the whole field of molecular dynamics (Siebrand 1976 Tully 1976 Child 1979 Rebentrost 1981 Baer 1983 Koppel, Domcke, and Cederbaum 1984 Whetten, Ezra, and Grant 1985 Desouter-Lecomte et al. 1985 Baer 1985b Lefebvre-Brion and Field 1986 Sidis 1989a,b Coalson 1989). The reasons will become apparent below. The two basic approaches, the adiabatic and the diabatic representations, will be outlined in Sections 15.1 and 15.2, respectively. Two examples, the photodissociation of CH3I and of H2S, will be discussed in Section 15.3. 

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

X-band cavity changes the fluorescence polarisation, which can be detected. The main features of the apparatus are illustrated in figure 11.12. One of the advantages of excitation with an electron beam, rather than with conventional monochromatic or white light sources, is that transitions between electronic states of different spin multiplicity are allowed consequently both singlet and triplet excited states can be populated. 

To show that this is the case we simplify the discussion of the optical excitation of the B — A — B molecule by focusing upon transitions between electronic states of the same representations, e.g., A to A or A" to A" (where A denotes the symmetric representation and A" the antisymmetric representation of the Cs group). We further assume that the ground vibronic state belongs to the A representation. To obtain control we choose the intermediate state E2) to be symmetric, and the intermediate state E ) to be antisymmetric, with respect to reflection in the a hyperplane. Hence we must first demonstrate that it is possible optically to excite, simultaneously, both the-symmetric E2) and antisymmetric E ) states from the ground state Eg). This requires the existence of both a symmetric dipole component, denoted ds, and an antisymmetric component, denoted da, with respect to reflection in the a hyperplane, because, by the symmetry properties of E2) and 1 ),... 

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