Electron-excitation states optically forbidden

Luminescence originates from electronically excited states in atoms and molecules and the emission process is governed by quantum mechanical selection rules. Forbidden transitions generally are slower than allowed optical transitions. Emission originating from allowed optical transitions, with decay times of the order of ps or faster is called fluorescence the term for emission with longer decay times is phosphorescence. The time in which the emission intensity decreases to 1/e or 1/10 (for exponential decay and hyperbolic decay, respectively) is called the decay time. 

Since the relaxation of the higher exciton states occurs on an ultrafast timescale of about 100 fs [23,26], the absorption spectrum for a closed structure, Fig. 26.4, top and centre, consists of either one or a few relatively broad spectral bands, respectively. For both cases, i.e., circular and elliptical arrangement, the transitions from the k = 1 exciton states are polarized perpendicular with respect to each other. Moreover, the lowest exciton state is optically forbidden, because a C2-type symmetry reduction alone, i.e., an ellipse, does not give rise to oscillator strength in the k = 0 state. This situation is reminescent to the electronically excited states of the B850 BChl a... 

Electronic HREELS Study. HREELS is mostly used as a vibrational spectroscopy and the extremely high resolution requirements are a consequence of that use. However, low energy electrons can be very useful to study the energy position and relative excitation probabilities of electronic states optically forbidden for spin or symmetry reasons. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

The contributions of optically forbidden electronic states to the x(3) of centrosymmetric structures are of particular interest. (18) Each of the terms in a sum-over-states calculation of x(3) involves the product of transition moments between a sequence of four states. There are symmetry selection rules that govern which states which can contribute to the individual terms. In a centrosymmetric molecule the symmetry of the contributing states must be in a sequence g -> u --> g --> u --> g.(19) This means that all the non-zero terms in the summation which determines the hyperpolarizibility must include an excited electronic state of g symmetry (or the ground state) as an intermediate state. The tetrakis(cumylphenoxy)phthalocyanines are approximately centrosymmetric and many of the new electronic states in a metal phthalocyanine will be of g symmetry. Such states may well contribute to the dependence of the hyperpolarizibility on metal substitution. 

Optical properties are usually related to the interaction of a material with electromagnetic radiation in the frequency range from IR to UV. As far as the linear optical response is concerned, the electronic and vibrational structure is included in the real and imaginary parts of the dielectric function i(uj) or refractive index n(oj). However, these only provide information about states that can be reached from the ground state via one-photon transitions. Two-photon states, dark and spin forbidden states (e.g., triplet) do not contribute to n(u>). In addition little knowledge is obtained about relaxation processes in the material. A full characterization requires us to go beyond the linear approximation, considering higher terms in the expansion of h us) as a function of the electric field, since these terms contain the excited state contribution. 

More General Treatments of Electron Correlation in Polymers.—The introduction of excitonic states was just a simple example to show how one can go beyond the HF approximation to obtain correlated electron-hole pairs, whose energy level(s) may fall into the forbidden gaps in HF theory, and form the basis for interpretation of optical phenomena in semiconducting polymers. The schemes described until now for investigation of certain types of correlation effects (the DODS method for ground-state properties and the exciton-picture for excited states) are relatively simple from both the conceptual and computational points of view and they have been actually used at the ab initio level. It is evident, on the other hand, that further efforts are needed in polymer electronic structure calculations if we want to reach the level of sophistication in correlation studies on polymers which is quite general nowadays in molecular quantum mechanics. 

The electronic transition to the MLCT and nn excited states are optically allowed transitions, and they have relatively large transition moments. They do not involve the population of an orbital that is antibonding with regard to the M—L bonds, in contrast to the forbidden transitions to the LF excited states. This is one of the reasons for photostability of Red) complexes. However, as discussed in the following sections, photoinduced chemical reactions have been reported in some cases, where transitions to reactive higher-energy states arise from photoexcitation with shorter wavelength irradiation or thermal activation from lowest excited state. 

Table 6-1. C h molecular point group. The electronic states of the flat Tg molecule are classified according to the two-fold screw axis (C2), inversion (z), and glide plane reflection (ct/,) symmetry operations. The and excited states transform like translations (7) along the molecular axes and are optically allowed. The Ag and It, states are isomorphous with the polarizability tensor components (a), being therefore one-photon forbidden and two-photon allowed.

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