Optically forbidden electronic states

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. 

Photoionization can also access excited electronic states of the ion that are difficult to study by optical methods. The photoionization yield of FeO increases dramatically 0.36 eV above the ionzation energy. This result corresponds to the threshold for producing low spin quartet states of FeO. These states had not been previously observed, as transitions to them are spin forbidden and occur at inconveniently low energy. Because the FeO + CH4 reaction occurs via low spin intermediates, accurately predicting the energies of high and low spin states is critical. 

Figure 28.1 The electronic structure of a solid can be described in terms of a band model in which bonding electrons are primarily found in a low-energy valence band, while conduction is typically associated with antibonding or nonbonding high-energy orbitals known as the conduction band. In the case of a semiconductor (left), these two bands are separated by a quantum-mechanical forbidden zone, the band gap. Excitation of electrons from the valence band to the conduction band gives rise to the bulk optical and electronic properties of the semiconductor. In the case of a metal (right), the conduction band and valence band overlap, giving rise to a continuum of states.

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... 

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... 

Fig. 1. The molecular energy level model used to discuss radiationless transitions in polyatomic molecules. 0O, s, and S0,S are vibronic components of the ground, an excited, and a third electronic state, respectively, in the Born-Oppenheimer approximation. 0S and 0 and 0j are assumed to be allowed, while transitions between j0,j and the thermally accessible 00 are assumed to be forbidden. The f 0n are the molecular eigenstates...

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.

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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