Two-electron excited states

FIGURE 3.8 Potential energy curves for the ground state and two electronically excited states in a hypothetical diatomic molecule. Predissociation may occur when the molecule is excited into higher vibrational levels of the state E and crosses over to repulsive state R at the point C (from Okabe, 1978). 

Direct calculation from equation (29) requires a knowledge of all excited-state wavefunctions. If these are known, equation (29) becomes a sum over all discrete states and an integration over continuum states. For systems of more than two electrons, excited-state wavefunctions are difficult to come by Even less is known about the continuum states, but for the diamagnetic susceptibility their contribution is thought to be of the same order of magnitude as that of the discrete states. For other systems the direct use of equation (29) is clearly a non-starter. 

Assuming a model wherein a molecule possesses only two electronically excited states, Schellman has proposed three mechanisms would lead to the observation of optical activity in the electronic transitions among these [9]. The three models may be summarized as ... 

The 5-term involves two electronic excited states (e and 5) and provides a mechanism for resonance-enhancement of non-totally symmetric vibrations. The 5-term, can be expressed as... 

Fig. 6. Non-adiabatic contributions to the scattering process are significant when the electronic energy separation of excited states e> and Is) is comparable to the vibrational energy level separation. In this case the coordinate operator, Q, may cause transitions between the vibrational manifolds of the two electronic excited states...

Formally, one can think of the Raman transition probability being proportional to the elements of the polarizability tensor of a bound electron as the exciting frequency approaches the resonance frequency, these elements are enhanced in a Lorentz model of the bound electron. A common example of this mechanism is furnished by the ring-breathing (in-plane expansion) modes of porphyrins. Another mechanism, called vibronic enhancement, involves vibrations which couple two electronic excited states. In both mechanisms, the enhancement factors are nearly proportional to the intensities in the absorption spectrum of the adsorbate. 

Several theories have been proposed to explain this photodissociation reaction. At present it is most reasonable to assume that at least two electronically excited states give rise to ICN absorption in the A continuum, one which correlates with I( i /2)+CN and one which correlates with I( i 3/2) + CN. The very hot rotational temperature observed probably results from the steep repulsive curve of the potential... 

In the preceding subsection, the interference effects between nuclear WPs of DCP were numerically treated. In this subsection, to confirm the interference effects, we present the results of an analytical treatment in a simplified one-dimensional model shown in Fig. 6.10. Here, q is the dimensionless normal coordinate of the effective breathing mode. The potentials in the ground and two electronic excited states (b and c, which correspond to L and H, respectively) were assumed to be displaced and undistorted ones. At least two vibrational eigenstates in each electronic state are needed for consideration of both the electronic and vibrational coherences in the simplified model. Here, b0(c0) and bl(cl) denote the lowest... 

The ground state of dioxygen is a triplet with two unpaired electrons with parallel spins. The first two electronically excited states are both sii lets, formed by relocation and/or pairing of the unpaired electrons in the 2pn antibonding orbitals. The half-filled antibonding molecular orbitals of 2 can accommodate two additional electrons. The addition of one electron affords the superoxide anion (O2 ) and two-electron reduction gives the peroxide ion (02 ). 

Figure 11.20 shows two electronically excited states for 1,3-butadiene and two electronically excited states for cyclobutene. In each case, the state labeled ES-1 is the excited state produced by moving one electron from the HOMO to the LUMO. For 1,3-butadiene, ES-1 has the configuration Ifs state... 

In 1969, a further development of the phenomenon was made [39] in which the relative quantum yields of fluorescence, were obtained for excitation of all the vibronic levels in the first two electronic excited states of 2,2-diethylchromene (I in Scheme 15.4). It was there found that c p showed variation as a function of (a) the electronic state, (b) the vibrational mode and (c) the vibrational level that was being excited. Comparison was made to a molecule of similar structure to 2,2-diethylchromene except the O atom was replaced by -CH2 (1,2-dihydronaphtha-lene, II in Scheme 15.4). In this case, excitation over 15 wavelengths, between 296 and 250 nm (first entire transition), did not result in any deviation ( 5 %) of c p and no photochemistry was observed over irradiation times comparable to that... 

To examine the effect of coherence on fluorescence anisotropy, consider a system with a ground state (state 1) and two electronically excited states (2 and 3), and assume as before that the interaction matrix elements 7/i2, T/is and H23 are zero in the absence of radiation. Suppose that an ensemble of systems in the ground state is excited with a weak pulse of light that is much shorter than the lifetime of the excited state (Ti). In the impulsive limit, the populatimi of excited state 2 generated by the pulse is... 

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