Optically forbidden states

Only the k = 0 state is optically allowed, and for attractive/repulsive J it lies at the bottom/top of the band. In attractive 7< 0 lattices the absorption spectrum is red-shifted with respect to Wq by 2J (J-aggregates), whereas a blue-shift by the same amount is expected for repulsive interactions (7 > 0, H-aggregates). The most impressive collective phenomenon in this simple model is recognized in the fluorescence behavior. In H-aggregates the fast relaxation of excited states to the bottom of the 1-exciton band leads to an optically forbidden state so that fluorescence is strongly suppressed in the material. In J-aggregates instead fluorescence is... 

Other predictions were that excited states produced in gases which are optically connected to the ground state would be found to be produced more rapidly than those for which optical transitions to the ground state are forbidden. In argon for example the production of optically forbidden states such as the Ap states (2p in Paschen notation) and the two metastable 3p 4s states (1 3 and I55) was predicted [3,5] to be delayed relative to the production of ions. 

For the cases of Ar2, Kr2, and Xe2 formation, Huffman and Katayama have shown that all optically accessible excited states whose energies lie above the threshold energy undergo homonuclear associative ionization. It would seem highly likely that the same statement would apply also to all optically forbidden states above threshold. Therefore, the electron-impact ionization-efficiency curves must be a superposition (weighted with respect to excitation cross sections) of the excitation functions of all excited states above threshold. 

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. 

All the transitions between ground-state 02 and the energetically accessible states are optically forbidden. The mercury-induced transition... 

Electronic transitions are optically forbidden only for large intemuclear distances r. For finite r, dipole transitions to the X 2 ground state are possible. They give rise to the well-known Hopfield continuum and 600-A emission and absorption bands.86 Only those collision partners that surmount the barrier of the ungerade potential are likely to radiate. The cross section for light emission65 is typically 10-4 A2, which is much too... 

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. 

This apparently is based on the assumption that the cross-section depends on exp (-AEjkT). However, Frish and Bochkova141 claim to have demonstrated that the 8P state is produced only in very low yield. They observed the emission from excited sodium atoms in an electric discharge in He, Hg and Na mixtures at very low total pressures. Their data appear to show that the cross-section for excitation of the 8P state, the process with the smallest energy discrepancy and for which optical transitions of both atoms are allowed, is smaller than the cross-section into the 9S state, which is optically forbidden for the sodium. 

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. 

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... 

It is worth noting that first-principles Time-Dependent Density-Functional Theory (TD-DFT) calculations on terthiophene-S,S-dioxide have also shown that another important result of the fxmctionalization of the thienyl ring with oxygen atoms is that the separation between the triplet state T2 and the singlet state SI is enhanced with respect to the parent unmodified terthiophene (Della Sala et 2003 Anni et al., 2005). In this way, the probability of intersystem crossing from singlet states to optically forbidden triplet states is reduced, advantaging further the PL efficiency. 

All the neutral single donors without d or f electrons have spin 1/2 while the double donors and acceptors have spin 0 in the ground state, but in some excited states, they have spin 1 and optically forbidden transitions between the singlet and triplet states have been observed. The spins of the neutral acceptors in the ground state depend on the electronic degeneracy of the VB at its maximum. For silicon, the threefold degeneracy of the valence band results in a quasi spin 3/2 of the acceptor ground state. 

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